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Quadratic Formula Calculator

Enter the coefficients a, b and c to solve ax² + bx + c = 0 — real or complex roots, with steps.

Reviewed by the OmniCalc teamMethod verified 2026-07-01

ax² + bx + c = 0

Result

x = 2 or 1

= discriminant D = 1

x = 2 or 1
Show steps
  1. Identify the coefficients: a = 1, b = -3, c = 2.
  2. Compute the discriminant D = b² − 4ac = -3² − 4·1·2 = 1.
  3. D > 0, so there are two distinct real roots.
  4. x = (−b ± √D) / (2a) = (3 ± 1) / 2.
  5. x₁ = 2, x₂ = 1.

How to use the quadratic formula calculator

  1. 1Enter the three coefficients a, b and c from ax² + bx + c = 0.
  2. 2Read the roots — two real, one repeated, or a complex pair.
  3. 3Open Show steps to see the discriminant and the formula applied.

Worked example

For x² − 3x + 2 = 0, the discriminant is 9 − 8 = 1 > 0, so there are two real roots: x = 2 or x = 1.

Frequently asked questions

What is the quadratic formula?

x = (−b ± √(b² − 4ac)) / (2a). It gives the roots of any equation of the form ax² + bx + c = 0, where a is not zero.

What does the discriminant tell me?

The discriminant D = b² − 4ac decides the roots: D > 0 gives two distinct real roots, D = 0 gives one repeated real root, and D < 0 gives a complex conjugate pair.

Why must a be non-zero?

If a = 0 there is no x² term, so the equation is linear (bx + c = 0), not quadratic. The tool flags this and asks for a non-zero leading coefficient.