Quadratic equation solver
Solve a × x² + b × x + c = 0 from its coefficients. See both real roots or the real and imaginary parts of a conjugate pair. Zero leading coefficients are handled as linear or constant equations.
Free to use. No email or account required.
Your inputs
The editable example is illustrative. Enter your own dimensions, operating data, prices, and fees. Results update as you edit.
Calculations run in your browser. Inputs are not saved or sent to analytics.
How it works
- x = (− ± √(² − 4 × × )) ÷ (2 × )
- Worked example
- a = 1; b = −3; c = 2 → x = 1, 2
Input and formula key
Your result
Complete the inputs to see your result.
Assumptions and limitations
Coefficients are scaled before evaluating the discriminant. A cancellation-resistant form computes real roots, but binary floating-point still limits accuracy near repeated roots. Complex roots are real part ± imaginary magnitude × i. This is a numerical solver, not a symbolic proof.
Sources
- OpenStax — mathematical formulas Sources reviewed: 2026-10-28
Processing and privacy
The calculation or transformation runs in your browser. The tool does not send its input values or generated output to an application server. Loading a page still makes infrastructure requests; optional analytics and Google consent messages have separate controls.
Privacy Policy. Privacy & preferences in the footer controls optional analytics.
Sources and maintenance
Maintained by emonster. Sources are listed with their own review dates; these are not live-data timestamps or claims of independent expert certification.
