Quadratic formula calculator
Solve ax² + bx + c = 0, including complex roots.
About this calculator
Enter a, b and c from your equation in the form ax² + bx + c = 0 to get its solutions.
A positive discriminant means two real solutions, zero means one repeated solution, and a negative value means two complex solutions.
How it works
Applies the quadratic formula. The discriminant b² − 4ac tells you whether the roots are real.
Worked example
- a: 1
- b: -3
- c: 2
Solution: x = 2, 1
The story behind it
Where the idea came from: Babylonian scribes, then Brahmagupta (628) and al-Khwarizmi (around 820).
Babylonian scribes were solving problems of this type about 4,000 years ago, usually framed as finding the sides of a field. Brahmagupta in India gave an explicit solution in 628, and al-Khwarizmi set out systematic methods in the book that gave us the word algebra. The formula on this page is their work in modern notation.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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