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When \( b^2 - 4ac = 0 \) there is one real root.

When \( b^2 - 4ac > 0 \) there are two real roots.

When \( b^2 - 4ac < 0 \) there are two complex roots.

## Quadratic Formula:

is used to solve quadratic equations where a ≠ 0 (polynomials with an order of 2)

## Quadratic Equation Calculator

Solve quadratic equations step-by-step.

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## Frequently Asked Questions (FAQ)

How do you calculate a quadratic equation.

## What is the quadratic formula?

## Does any quadratic equation have two solutions?

## What is quadratic equation in math?

## How do you know if a quadratic equation has two solutions?

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## Quadratic Formula Calculator

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## Example (Click to try)

About the quadratic formula, quadratic formula video lesson.

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## Quadratic Formula Calculator

The calculator below solves the quadratic equation of ax 2 + bx + c = 0 .

## Derivation of the Quadratic Formula

From this point, it is possible to complete the square using the relationship that:

Continuing the derivation using this relationship:

## Quadratic Equation Solver

## Is it Quadratic?

Only if it can be put in the form ax 2 + bx + c = 0 , and a is not zero .

The name comes from "quad" meaning square, as the variable is squared (in other words x 2 ).

These are all quadratic equations in disguise:

## How Does this Work?

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 !

- when it is positive, we get two real solutions,
- when it is zero we get just ONE solution,
- when it is negative we get complex solutions.

Learn more at Quadratic Equations

Note: you can still access the old version here .

## Quadratic Formula Calculator

Enter the equation you want to solve using the quadratic formula.

Quadratic Formula : x = − b ± b 2 − 4 a c 2 a

Solve Using the Quadratic Formula Apply the Quadratic Formula

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## Online Equation Solver

Solve linear, quadratic and polynomial systems of equations with wolfram|alpha.

## More than just an online equation solver

## Tips for entering queries

- find roots to quadratic x^2-7x+12
- plot inequality x^2-7x+12<=0
- solve {3x-5y==2,x+2y==-1}
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- solve 3x^2-y^2==2 and x+2y^2==5
- plot 3x^2-y^2>=2 and x+2y^2<=5
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## About solving equations

A value is said to be a root of a polynomial if ..

## How Wolfram|Alpha solves equations

## 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:.

## An equation root calculator that shows steps

## Solved quadratic equation examples

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

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

Go to Solved Algebra examples with Steps

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## Online calculator. Quadratic equation solver.

This online calculator will help you to solve quadratic equation.

## Quadratic equation solver

Guide how to enter data into the quadratic equation solver:.

## Additional features of the quadratic equation solver

## Rules. Quadratic equation.

## Quadratic Formula.

Expression (∆ = b 2 - 4 a c ) is called the discriminant .

- If the discriminant is positive (∆ > 0), then there are two distinct roots, both of which are real numbers.
- If the discriminant is zero (∆ = 0), then there is exactly one distinct real root, sometimes called a double root ( x 1 = x 2 ).
- If the discriminant is negative (∆ < 0), then there are no real roots.

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The four steps for solving an equation include the combination of like terms, the isolation of terms containing variables, the isolation of the variable and the substitution of the answer into the original equation to check the answer.

To calculate the discriminant of a quadratic equation, put the equation in standard form. Substitute the coefficients from the equation into the formula b^2-4ac. The value of the discriminant indicates what kind of solutions that particular...

Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find an...

This online calculator is a quadratic equation solver that will solve a second-order polynomial equation such as ax2 + bx + c = 0 for x, where a ≠ 0

To solve a quadratic equation, use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). What is the quadratic formula? The quadratic formula gives solutions

What do you want to calculate? · Solve · Solve for Variable · Practice Mode · Simplify · Factor · Step-By-Step · Evaluate · Graph

A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. Only the use of the

How Does this Work? · when it is positive, we get two real solutions, · when it is zero we get just ONE solution, · when it is negative we get complex solutions.

Enter the equation you want to solve using the quadratic formula. The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients

Wolfram|Alpha can apply the quadratic formula to solve equations coercible into the form ax2+bx

Free Online Equation Calculator helps you to solve linear, quadratic and polynomial systems of equations. Answers, graphs, alternate forms.

Enter the coefficients for the Ax2 + Bx + C = 0 equation and Quadratic Equation will output the solutions (if they are not imaginary).

A quadratic is a second degree polynomial of the form: $ax^2+bx+c=0$ a x 2+ b x + c =0 where $a\ne0$ a ≠0. To solve an equation using the online calculator

This online calculator will help you to solve quadratic equation. Using this online calculator, you will receive a detailed step-by-step solution to your