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Quadratic Formula Roots and Discriminant Calculator

x = (−b ± √(b²−4ac)) / (2a) — real and complex roots.

Solves ax² + bx + c = 0 using the quadratic formula. Returns both roots, the discriminant Δ = b²−4ac (positive = 2 real, zero = repeated, negative = complex), and vertex.

Nadia Almasri By Nadia Almasri
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

x = (−b ± √Δ) / (2a); Δ = b² − 4ac

In depth

Solves ax² + bx + c = 0 using the quadratic formula. Returns both roots, the discriminant Δ = b²−4ac (positive = 2 real, zero = repeated, negative = complex), and vertex.