How to calculate quadratic
x = (−b ± √(b² − 4ac)) ÷ 2a
Worked example. Two real roots: 1 discriminant.
Example inputs — a: 1; b: -3; c: 2. Starting values are illustrative.
x = 2 or x = 1
From George Guju, founder of Calculyn · Educational calculator guidance, not professional advice.
How it works
The discriminant (b² − 4ac) tells you how many real solutions there are: positive means two, zero means one, negative means two complex roots.
Assumptions & limitations
- Results are rounded for display.
Formula and assumptions reviewed October 2026 by the Calculyn team. How we build our calculators
Frequently asked questions
What's the vertex?
The highest or lowest point of the parabola y = ax² + bx + c.