Quadratic Formula Calculator
Solve ax² + bx + c = 0 — both roots and the discriminant, step by step.
- Discriminant (b² − 4ac)1.0000
- Root x₁2.0000
- Root x₂1.0000
Inputs used
- a (x² coefficient)1
- b (x coefficient)-3
- c (constant)2
About this calculator
The quadratic formula solves any equation of the form ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) ÷ 2a. The two signs of the ± give the two roots.
The discriminant, b² − 4ac, tells you what to expect before solving: positive means two distinct real roots, zero means one repeated root (both answers below will match), and negative means the roots are complex — this calculator reports an error in that case, since there's no real solution to show.
The coefficient a can't be zero (that's a linear equation, not a quadratic — solve −c/b directly). Sign mistakes on b and c are the most common source of wrong answers: match the equation form exactly.
Results are informational only — not financial, medical or legal advice.