Quadratic Formula Calculator
Find real and complex roots of any quadratic equation using the quadratic formula, with the discriminant explained.
Example values are shown — change any of them and the answer updates live.
Roots
x₁ = 2 · x₂ = 1
1x² + -3x + 2 = 0
Discriminant1 (two real)
Vertex(1.5, -0.25)
Axis of symmetryx = 1.5
Exact quadratic formula — complex roots shown when the discriminant is negative.
Real vs complex roots
x² − 3x + 2
x₁ = 2 · x₂ = 1
two real roots
x² − 2x + 5
x₁ = 1 + 2i · x₂ = 1 − 2i
complex roots
Discriminant
1
Roots
Step 1 · Discriminant
Δ = b² − 4ac
(-3)² − 4·(1)·(2)
1
Step 2 · Roots
x = (−b ± √Δ) ÷ 2a
(−(-3) ± √1) ÷ 2·(1)
x₁ = 2 · x₂ = 1
Exact arithmetic — computed instantly in your browser.