Quadratic Formula Calculator
Solve quadratic equations ax² + bx + c = 0 with step-by-step work. Free online Quadratic Formula Calculator for algebra — instant, accurate results, no signup.
Equation: 1x² + -5x + 6 = 0
Derivation
- ├── 01Given
a = 1, b = -5, c = 6 - ├── 02Formula
x = (−b ± √(b² − 4ac)) / (2a) - ├── 03Discriminant
b² − 4ac = -5² − 4·1·6 = 25 − 24 = 1 - ├── 04√Discriminant
√1 = 1.0000 - ├── 05Substitute
(−-5 ± 1.0000) / (2·1) - ├── 06Root 1 (+)3.0000
- └── 07Root 2 (−)2.0000
The quadratic formula goes back to Babylonian scribes c. 2000 BCE; al-Khwārizmī gave it in words in 820 CE; Viète wrote it in algebraic symbols in 1591.
Understanding the Quadratic Formula Calculator
The Quadratic Formula Calculator helps you compute solve quadratic equations ax² + bx + c = 0 with step-by-step work.. It runs entirely in your browser with no sign-up required.
Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The Quadratic Formula Calculator sits in that toolkit — it solve quadratic equations ax² + bx + c = 0 with step-by-step work. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.
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