Quadratic Formula Calculator
Solve ax² + bx + c = 0 exactly: rational, surd and complex roots, with the discriminant and vertex.
Change the values and press Calculate to work out your own figures.
Enter a, b and c (fractions allowed).
Show the working
- x = (−b ± √(b² − 4ac)) ÷ 2a
- b² − 4ac = 16
- x = -2/3, x = -2
How to use it
Enter a, b and c (fractions allowed).
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
x = (−b ± √(b² − 4ac)) ÷ 2a
The discriminant
b² − 4ac > 0: two real roots; = 0: one; < 0: two complex roots.
Questions
Roots of 3x² + 8x + 4?
−2/3 and −2.
What if a = 0?
It isn't quadratic; solve bx + c = 0 instead.
Formulas
x = (−b ± √(b² − 4ac)) ÷ 2a
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).