## Online Quadratic Formula Calculator

Apply the quadratic formula using wolfram|alpha, a useful tool for finding the solutions to quadratic equations.

2 + b x + c = 0 . In doing so, Wolfram|Alpha finds both the real and complex roots of these equations. It can also utilize other methods helpful to solving quadratic equations, such as completing the square, factoring and graphing.

Learn more about:

- Quadratic formula

## Tips for entering queries

Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask about finding roots of quadratic equations.

- quadratic formula 4x^2 + 4 x - 8
- quadratic formula a = 1, b = -1, c = 2
- solve x^2 - x - 4 = 0
- solve x^2 - 3x - 4 = 0
- View more examples

## Access instant learning tools

Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator

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## What are quadratic equations, and what is the quadratic formula?

A quadratic is a polynomial of degree two..

Quadratic equations form parabolas when graphed, and have a wide variety of applications across many disciplines. In physics, for example, they are used to model the trajectory of masses falling with the acceleration due to gravity.

Situations arise frequently in algebra when it is necessary to find the values at which a quadratic is zero. In other words, it is necessary to find the zeros or roots of a quadratic, or the solutions to the quadratic equation. Relating to the example of physics, these zeros, or roots, are the points at which a thrown ball departs from and returns to ground level.

b 2 - 4 a c 2 a , determines the one or two solutions to any given quadratic. Sometimes, one or both solutions will be complex valued.

Discovered in ancient times, the quadratic formula has accumulated various derivations, proofs and intuitions explaining it over the years since its conception. Some involve geometric approaches. Others involve analysis of extrema. There are also many others. Those listed and more are often topics of study for students learning the process of solving quadratic equations and finding roots of equations in general.

Alternative methods for solving quadratic equations do exist. Completing the square, factoring and graphing are some of many, and they have use cases—but because the quadratic formula is a generally fast and dependable means of solving quadratic equations, it is frequently chosen over the other methods.

## Quadratic Equation Solver

What do you want to calculate.

- Solve for Variable
- Practice Mode
- Step-By-Step

## Step-By-Step Example

Example (click to try), choose your method, solve by factoring.

Example: 3x^2-2x-1=0

## Complete The Square

Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.)

## Take the Square Root

Example: 2x^2=18

## Quadratic Formula

Example: 4x^2-2x-1=0

## About quadratic equations

Need more problem types? Try MathPapa Algebra Calculator

Clear Quadratic Equation Solver »

## Quadratic equation root calculator

Want to calculate? Get Solutions Here:

Enter a math problem on an Equation in the text area Above

Example x^2-2x+3=4 -OR- 2x-y=9 Click the button to Solve!

## Graphical Solution of Equations:

A worked example to illustrate how the quadratic calculator works:.

This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation. A quadratic is a second degree polynomial of the form: ax^2+bx+c=0 where a\neq 0 . To solve an equation using the online calculator, simply enter the math problem in the text area provided. Hit the calculate button to get the roots. A quadratic equation has two roots or zeroes namely; Root1 and Root2.

## An equation root calculator that shows steps

Learning math with examples is the best approach. With our online calculator, you can learn how to find the roots of quadratics step by step. First, find the roots or solutions your way, and then use the roots calculator to confirm your answer. The calculator uses the quadratic formula to find the roots of a quadratic equation.

## Solved quadratic equation examples

x^2 -6x + 3 = 0

x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }

x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(1)(3)}}{ 2(1) }

x = \dfrac{ 6 \pm \sqrt{36 - 12}}{ 2 }

x = \dfrac{ 6 \pm \sqrt{24}}{ 2 }

x = \frac{ 6 \pm 2 \sqrt{6}}{ 2 }

x = = 3+\sqrt{6} Or x = 3- \sqrt{6}

## Need to learn Algebra through examples?

Find more quadratic formula calculator Solved Examples Here:

How the Quadratic formula root calculator works

The online roots calculator is simple to use. Furthermore, the calculator can be used to find roots of varied problems. Whether the roots are real or complex, the calculator is able show a step by step solution.

To use this calculator, Insert your math expression on the textarea provided. Note you should only use the allowed notations and characters in order to obtain correct solution. Once you have the right expression or equation, Hit the calculate button to get started. The calculator will show you all the steps together with the reasoning or explanation behind each of the steps.

Acceptable Math symbols and their usage If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators.

- + Used for Addition
- - Used for Subtraction
- * multiplication operator symbol
- / Division operator
- ^ Used for exponent or to Raise to Power
- sqrt Square root operator

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## Quadratic Formula Calculator

What is the quadratic formula, coefficients of a quadratic equation, how to use the quadratic formula solver, solving quadratic equations with a negative determinant, extra resources.

If you need to solve an equation of the form Ax² + Bx + C = 0 , this quadratic formula calculator is here to help you. With just a few clicks, you will be able to solve even the most challenging problems. This article describes in detail what is the quadratic formula and what the symbols A, B, and C stand for. It also explains how to solve quadratic equations, which have a negative determinant and no real roots.

The quadratic formula is the solution of a second-degree polynomial equation of the following form:

Ax² + Bx + C = 0

If you can rewrite your equation in this form, it means that it can be solved with the quadratic formula. A solution to this equation is also called a root of an equation.

The quadratic formula is as follows:

x = (-B ± √Δ)/2A

- Δ = B² – 4AC

Using this formula, you can find the solutions to any quadratic equation. Note that there are three possible options for obtaining a result:

The quadratic equation has two unique roots when Δ > 0. Then, the first solution of the quadratic formula is x₁ = (-B + √Δ)/2A , and the second is x₂ = (-B – √Δ)/2A .

The quadratic equation has only one root when Δ = 0. The solution is equal to x = -B/2A . It is sometimes called a repeated or double root.

The quadratic equation has no real solutions for Δ < 0.

You can also graph the function y = Ax² + Bx + C . It's shape is a parabola, and the roots of the quadratic equation are the x-intercepts of this function.

💡 We use the quadratic formula in many fields of our life, not only mathematics or physics but also construction. For example, you can plan a smooth transition between two sloped roadways using the vertical curve formula which bases on the quadratic equation.

A, B, and C are the coefficients of the quadratic equation. They are all real numbers, not dependent on x. If A = 0, then the equation is not quadratic, but linear.

If B² < 4AC , then the determinant Δ will be negative. It means that such an equation has no real roots.

Write down your equation. Let's assume it is 4x² + 3x – 7 = -4 – x .

Bring the equation to the form Ax² + Bx + C = 0 . In this example, we will do it in the following steps:

4x² + 3x - 7 = -4 – x

4x² + (3 + 1)x + (-7 + 4) = 0

4x² + 4x - 3 = 0

Calculate the determinant.

Δ = B² – 4AC = 4² - 4×4×(-3) = 16 + 48 = 64 .

Decide whether the determinant is greater, equal, or lower than 0. In our case, the determinant is greater than 0, which means that this equation has two unique roots.

Calculate the two roots using the quadratic formula.

x₁ = (-B + √Δ)/2A = (-4 +√64) / (2×4) = (-4 + 8) / 8 = 4/8 = 0.5

x₂ = (-B – √Δ)/2A= (-4 -√64) / (2×4) = (-4 – 8) / 8 = -12/8 = -1.5

The roots of your equation are x₁ = 0.5 and x₂ = -1.5 .

You can also simply type the values of A, B, and C into our quadratic equation calculator and let it perform all calculations for you.

Make sure you have written down the correct number of digits using our significant figures calculator .

Even though the quadratic formula calculator indicates when the equation has no real roots, it is possible to find the solution of a quadratic equation with a negative determinant. These roots will be complex numbers .

Complex numbers have a real and imaginary part. The imaginary part is always equal to the number i = √(-1) multiplied by a real number.

The quadratic formula remains the same in this case.

Notice that, as Δ < 0, the square root of the determinant will be an imaginary value. Hence:

Re(x) = -B/2A

Im(x) = ± (√Δ)/2A

An alternative way of dealing with quadratic equations is factoring trinomials . And it really helps if you're able to quickly recognize perfect square trinomials . The next step is to learn how to graph quadratic inequalities .

If, after learning all about solving quadratic equations, you still want more math? Omni has over 240 math calculators to explore. In particular, we recommend you take a look at our cubic equation solver . We also recommend you check out the Computer Technology For Math Excellence's webpage . They have a vast collection of resources to learn all about math, with particular attention to the Common Core curriculum.

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## Quadratic Equation Calculator

Quadratic formula, quadratic equation example.

## Quadratic Formula Calculator

Our quadratic equation calculator is here to find solutions (roots) and check your work—but it does not provide any shortcuts. Even though our calculator is efficient at finding an answer to your problems, it doesn’t reveal any of the steps involved in solving a quadratic equation. To better learn how to solve the equations on your own—and because practice helps improve your skills—we encourage you to solve the problems on your own first and use our calculator to make sure your answer is correct last.

## How to Use the Quadratic Equation Calculator

To use the calculator:

- Enter the corresponding values into the boxes below and click Solve.
- The results will appear in the boxes labeled Root 1 and Root 2 . For example, for the quadratic equation below, you would enter 1, 5 and 6.
- After pressing Solve , your resulting roots would be -2 and -3.
- Click Reset to clear the calculator and enter new values.

## IMAGES

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## COMMENTS

Free Equation Given Roots Calculator - Find equations given their roots step-by-step

The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. Calculator determines whether the discriminant \( (b^2 - 4ac) \) is less than, greater than or equal to 0. When \( b^2 - 4ac = 0 \) there is one real root. When \( b^2 - 4ac > 0 \) there are two real roots. When \( b^2 ...

A useful tool for finding the solutions to quadratic equations. Wolfram|Alpha can apply the quadratic formula to solve equations coercible into the form ax 2 + bx + c = 0. In doing so, Wolfram|Alpha finds both the real and complex roots of these equations. It can also utilize other methods helpful to solving quadratic equations, such as ...

Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.) Take the Square Root. Example: 2x^2=18. Quadratic Formula. Example: 4x^2-2x-1=0. About quadratic equations Quadratic equations have an x^2 term, and can be rewritten to have the form: a x 2 + b x + c = 0. Need more problem types?

A quadratic is a second degree polynomial of the form: ax2 + bx + c = 0 where a ≠ 0. To solve an equation using the online calculator, simply enter the math problem in the text area provided. Hit the calculate button to get the roots. A quadratic equation has two roots or zeroes namely; Root1 and Root2.

The quadratic formula is the solution of a second-degree polynomial equation of the following form: Ax² + Bx + C = 0. If you can rewrite your equation in this form, it means that it can be solved with the quadratic formula. A solution to this equation is also called a root of an equation. The quadratic formula is as follows: x = (-B ± √Δ ...

Quadratic Formula. The calculator uses the following formula: x = (-b ± √ D) / 2a, where D = b 2 - 4ac. This formula calculates the solution of quadratic equations (ax 2 +bx+c=0) where x is unknown, a is the quadratic coefficient (a ≠ 0), b is the linear coefficient and c represents the equation's constant. The letters a, b and c are known numbers and are the quadratic equation's ...

The results will appear in the boxes labeled Root 1 and Root 2. For example, for the quadratic equation below, you would enter 1, 5 and 6. After pressing Solve, your resulting roots would be -2 and -3. Click Reset to clear the calculator and enter new values. x 2 + 5x + 6 = 0. Enter the coefficient of x 2 here. Enter the coefficient of x here.

Quadratic Formula Steps. There are several steps you have to follow in order to successfully solve a quadratic equation: Step 1: Identify the coefficients. Examine the given equation of the form \ (ax^2+bx+c\), and determine the coefficients \ (a\), \ (b\) and \ (c\). The coefficient \ (a\) is the coefficient that appears multiplying the ...

Step 1: Enter the equation you want to solve using the quadratic formula. The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients. For equations with real solutions, you can use the graphing tool to visualize the solutions. Quadratic Formula: x = −b±√b2 −4ac 2a x = − b ± b 2 − 4 a c 2 a.

In algebra, a quadratic equation is any polynomial equation of the second degree with the following form: ax 2 + bx + c = 0. where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. The numerals a, b, and c are coefficients of the equation, and they represent known numbers. For example, a cannot be 0, or the equation would be linear ...

The calculator on this page shows how the quadratic formula operates, but if you have access to a graphing calculator you should be able to solve quadratic equations, even ones with imaginary solutions.. Step 1) Most graphing calculators like the TI- 83 and others allow you to set the "Mode" to "a + bi" (Just click on 'mode' and select 'a+bi').

Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Quadratic Equation Solver. Save Copy. Log InorSign Up "Change the coefficients of your quadratic equation useing the sliders below. ... Roots. 18. 68. powered by. powered by "x" x "y" y "a" squared a 2 "a ...

The quadratic equation can have either one or two real roots, or two complex roots, depending on the values of the coefficients a, b, and c. The quadratic formula is used to calculate the roots of the quadratic equation, and it is given by: x = (-b ± √ (b^2 - 4ac)) / 2a. The solutions to the quadratic equation can also be found by ...

The solution (s) to a quadratic equation can be calculated using the Quadratic Formula: The "±" means we need to do a plus AND a minus, so there are normally TWO solutions ! The blue part ( b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer: when it is negative we get complex solutions.

This method can be used to solve all types of quadratic equations, although it can be complicated for some types of equations. The method involves seven steps. Example 04: Solve equation $ 2x^2 + 8x - 10= 0$ by completing the square. Step 1: Divide the equation by the number in front of the square term.

Free equations calculator - solve linear, quadratic, polynomial, radical, exponential and logarithmic equations with all the steps. Type in any equation to get the solution, steps and graph

A quadratic equation solver is a free step by step solver for solving the quadratic equation to find the values of the variable. With the help of this solver, we can find the roots of the quadratic equation given by, ax 2 + bx + c = 0, where the variable x has two roots. The solution is obtained using the quadratic formula;. where a, b and c are the real numbers and a ≠ 0.

SolutionStep 1 Put the equation in standard form. We must subtract 6 from both sides. Step 2 Factor completely. Recall how to factor trinomials. Step 3 Set each factor equal to zero and solve for x. Since we have (x - 6) (x + 1) = 0, we know that x - 6 = 0 or x + 1 = 0, in which case x = 6 or x = - 1.

Quadratic equation calculator. Quadratic equation has the basic form: ax2 + bx+ c = 0. Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant. a =.

The quadratic formula says the roots of a quadratic equation ax 2 + bx + c = 0 are given by x = (-b ± √ (b 2 - 4ac)) /2a. To solve any quadratic equation, convert it into standard form ax 2 + bx + c = 0, find the values of a, b, and c, substitute them in the roots of quadratic equation formula and simplify.

Solve Quadratic Equation using the Quadratic Formula 6.3 Solving x 2-3x+2 = 0 by the Quadratic Formula . According to the Quadratic Formula, x , the solution for Ax 2 +Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by : - B ± √ B 2-4AC x = ————————

A useful tool for finding the solutions to quadratic equations. Wolfram|Alpha can apply the quadratic formula to solve equations coercible into the form ax2 +bx+c= 0 a x 2 + b x + c = 0. In doing so, Wolfram|Alpha finds both the real and complex roots of these equations. It can also utilize other methods helpful to solving quadratic equations ...

The two roots in the quadratic formula are presented as a single expression. The positive sign and the negative sign can be alternatively used to obtain the two distinct roots of the equation. Quadratic Formula: The roots of a quadratic equation ax 2 + bx + c = 0 are given by x = [-b ± √(b 2 - 4ac)]/2a.

For the values k = 9 and k = -9 the roots of the quadratic equation . 3x²+ 2kx + 27 = 0 real and equal.. What is quadratic equation? Any equation in algebra that can be rearranged in standard form as: [tex]ax^2 + bx + c = 0[/tex] is known as a quadratic equation (from the Latin quadratus, "square").. where a ≠ 0 and a, b, and c are known numbers, x is an unknown value, and a.