Fast Algebra Solver

Quadratic Equation Calculator

Solve any equation in the standard form ax² + bx + c = 0. Enter the values of a, b, and c to get exact roots, the discriminant, and clear step-by-step calculation instantly.

Enter Equation Values

ax² + bx + c = 0

Result

Enter values for a, b, and c to solve your quadratic equation.

Instant Solution

Get roots immediately using the quadratic formula without manual calculation errors.

Step-by-Step Method

See the discriminant, formula substitution, and final answer in a clean format.

Real & Complex Roots

The calculator supports real roots, equal roots, and complex imaginary roots.

What Is a Quadratic Equation Calculator?

A Quadratic Equation Calculator is an online math tool that solves equations written in the form ax² + bx + c = 0. Instead of solving the equation manually, you only need to enter the values of a, b, and c. The calculator then applies the quadratic formula and shows the roots of the equation.

This tool is useful for students, teachers, engineers, and anyone working with algebra problems. It can handle equations with two real roots, one repeated root, or complex roots when the discriminant is negative.

Quadratic Formula

The calculator uses the standard quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this formula, b² - 4ac is called the discriminant. It tells whether the equation has two different real roots, one repeated real root, or two complex roots.

How It Works

Enter the value of a, which is the coefficient of x².
Enter the value of b, which is the coefficient of x.
Enter the value of c, which is the constant number.
Click the calculate button to solve the equation.
The tool calculates the discriminant and displays the roots.

Example

For the equation x² - 5x + 6 = 0, the values are: a = 1, b = -5, and c = 6. The calculator finds the roots as x = 3 and x = 2.

Note: The value of a cannot be zero. If a = 0, the equation is not quadratic.

Frequently Asked Questions

A quadratic equation is a second-degree equation written as ax² + bx + c = 0, where a, b, and c are numbers and a is not zero.

The discriminant is b² - 4ac. If it is positive, the equation has two real roots. If it is zero, it has one repeated root. If it is negative, it has complex roots.

Yes. If the discriminant is negative, the calculator shows the roots in complex form using the imaginary unit i.

If a is zero, the equation no longer contains an x² term, so it becomes a linear equation instead of a quadratic equation.

Yes, this calculator is completely free to use and works directly in your browser without requiring installation.