Math & Science
Quadratic Equation Solver
Solve quadratic equations and find roots
Formulas and edge cases are reviewed against authoritative references before publication. For methodology, editorial standards, or corrections, use the links below.
Frequently asked questions
What is the discriminant?
D = b² - 4ac determines root type: D>0 = two real, D=0 = one real, D<0 = complex.
What is the vertex?
The minimum/maximum point of the parabola at x = -b/(2a).
Can I solve higher degree equations?
This tool is for quadratics only. Cubics and above require different methods.
Related tools
About this tool
Inputs
- Coefficient a
- Coefficient b
- Coefficient c
- Two real roots
- One real root
- Complex roots
- Linear equation
- Not a quadratic
Results
- Roots (x values)
- Discriminant
- Root Type
- Vertex
- Axis of Symmetry
Before making a decision based on estimates, run the numbers through this Quadratic Equation Solver. A few seconds of input can save hours of uncertainty. The required inputs are coefficient a, coefficient b, coefficient c, two real roots, one real root, complex roots, linear equation and not a quadratic. Once provided, the result — roots (x values), discriminant, root type and other key metrics — appears instantly. The ability to solve quadratic equations and find roots comes up more often than most people expect — in professional work, academic projects, and everyday planning.
When in doubt, estimate the answer first so you have a sanity check for the exact result. Mathematical tools turn abstract formulas into concrete answers you can verify and apply. D = b² - 4ac determines root type: D>0 = two real, D=0 = one real, D<0 = complex. Every calculator on this page uses a well-defined formula — the same one you would find in a textbook, applied instantly. Precision matters: rounding at intermediate steps can introduce errors that compound in multi-step calculations. If the result surprises you, revisit your inputs — a mistyped digit or wrong unit is usually the culprit.