How does this solve quadratic equations?

Using the quadratic formula: x = (−b ± √(b²−4ac)) ÷ 2a.

What does the discriminant tell you?

Positive means two real solutions; zero means one repeated solution; negative means two complex solutions.

Can a quadratic equation have no real solutions?

Yes — a negative discriminant means the solutions are complex, so the parabola never crosses the x-axis.

Quadratic Equation Calculator - Solve ax² + bx + c = 0

Quadratic Equation Calculator

Solve any quadratic equation ax² + bx + c = 0 using the quadratic formula.

a x² + b x + c = 0

Discriminant (Δ)-

Root x1-

Root x2-

What Is a Quadratic Equation Calculator?

This calculator solves any quadratic equation in the standard form ax² + bx + c = 0, returning its two roots (real or complex) using the quadratic formula.

Formula

The quadratic formula is: x = [−b ± √(b² − 4ac)] / 2a. The term (b² − 4ac) is called the discriminant (Δ):

If Δ > 0, there are two distinct real roots.
If Δ = 0, there is exactly one repeated real root.
If Δ < 0, the roots are complex (involve the imaginary unit i).

How to Use This Calculator

Enter the coefficients a, b, and c from your equation ax² + bx + c = 0.
Click Calculate to see the discriminant and both roots.

Worked Example

For x² − 3x + 2 = 0 (a = 1, b = −3, c = 2), the discriminant is (−3)² − 4×1×2 = 9 − 8 = 1. The roots are x = (3 ± 1) / 2, giving x1 = 2 and x2 = 1. Enter a = 1, b = -3, c = 2 above to confirm.

Common Uses

Quadratic equations appear throughout algebra, physics (projectile motion), engineering, and economics wherever a relationship involves a squared variable.