What is the discriminant?

The discriminant b^2 - 4ac tells whether a quadratic has two, one, or no real roots.

Does this calculator factor the quadratic?

It uses the quadratic formula. For factoring-focused steps, use the factoring calculator.

Algebra

Quadratic Equation Calculator with Steps

Solve ax^2 + bx + c = 0 using the quadratic formula, with discriminant, real roots, and answer checks.

Solve ax^2 + bx + c = 0

abc

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Answer

x = 3 or x = 2

Discriminant = b^2 - 4ac = 1
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
$x = (5 \pm 1) /2$
Check x1: 0
Check x2: 0

How to use the quadratic equation calculator

The quadratic equation calculator is built for high-school algebra. It calculates the discriminant, identifies the number of real roots, and shows the formula substitution.

Enter a, b, and c for ax^2 + bx + c = 0.
Compute the discriminant b^2 - 4ac.
Substitute into the quadratic formula.
Check roots by evaluating the original expression.

Formula or method

x = (-b +/- sqrt(b^2 - 4ac)) / (2a).

Worked examples

Two real roots

Problem: x^2 - 5x + 6 = 0

Solution: Discriminant is 1, so x = 2 or x = 3.

No real roots

Problem: x^2 + 1 = 0

Solution: Discriminant is -4, so there are no real roots.