What is the quadratic formula?

For ax² + bx + c = 0 with a ≠ 0, x = (−b ± √(b² − 4ac)) / 2a. The expression b² − 4ac is called the discriminant.

What does the discriminant tell me?

If discriminant > 0: two distinct real roots. If = 0: one repeated real root. If < 0: two complex-conjugate roots (no real solution).

What happens if a = 0?

The equation is no longer quadratic — it becomes linear (bx + c = 0) and has a single root x = −c/b, which this calculator will return.

Quadratic Equation Solver

Calculators· 14 tools

Free quadratic equation solver. Enter coefficients a, b, c and get the roots (real or complex), discriminant, axis of symmetry, and vertex of the parabola. Uses the quadratic formula with step-by-step output. Handles double roots and complex-conjugate pairs.

Solve ax² + bx + c = 0

1x² -5x +6 = 0

Roots

x₁ = 2

x₂ = 3

Discriminant

Axis of symmetry

x = 2.5

Vertex

(2.5, -0.25)

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