Quadratic Equation Solver - ax² + bx + c = 0 (Real & Complex Roots)
Solve any quadratic ax² + bx + c = 0 - real or complex roots, discriminant, and vertex
How it works
- 1Enter a, b, c
The three coefficients of ax² + bx + c = 0. Any real numbers, positive or negative.
- 2Read the roots
Two real, one repeated, or two complex conjugate roots depending on the discriminant.
- 3See vertex and discriminant
Vertex tells you the parabola's minimum or maximum point. Discriminant (b²−4ac) sign classifies the roots.
About Quadratic Equation Solver - ax² + bx + c = 0 (Real & Complex Roots)
Free quadratic equation solver. Enter the coefficients a, b, and c of ax² + bx + c = 0 to see the roots (real or complex), the discriminant, and the vertex coordinates of the parabola. Handles all three discriminant cases: two real roots, one repeated root, or two complex conjugate roots. Runs entirely in your browser. Quadratic Equation Solver - ax² + bx + c = 0 (Real & Complex Roots) on 712 Tools runs entirely inside your browser using modern JavaScript APIs - no server ever sees your data. That means instant results, complete privacy, and no upload limits.
Whether you need to solve any quadratic ax² + bx + c = 0 - real or complex roots, discriminant, and vertex for a debugging session, a quick sanity check, or a production incident, this tool is free to use as many times as you need. There are no watermarks, no sign-up, and no ads inside the tool itself.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b²−4ac)) ÷ 2a. The ± gives two solutions when the discriminant is positive.
What happens if a = 0?
The equation is linear, not quadratic. The tool solves x = −c ÷ b when b is non-zero.
What are complex roots?
When b² − 4ac < 0 the square root is imaginary, giving two complex conjugate solutions of the form p ± qi.
Related tools
Percentage Calculator
What is X% of Y, X is what % of Y, percent increase, decrease, and change
Mortgage Calculator
Estimate your monthly mortgage payment, total interest, and full amortization schedule
Loan / EMI Calculator
Calculate monthly EMI, total interest, and total payable for any personal, auto, or student loan
BMI Calculator
Calculate Body Mass Index from height and weight - metric (cm/kg) or imperial (ft·in/lb)
Age Calculator
Calculate exact age in years, months, and days from any date of birth to any date
Date Calculator
Calculate days between two dates, or add/subtract days, weeks, months, or years from any date