Quadratic Formula Calculator
Enter the coefficients a, b, and c to solve a quadratic equation for x, including complex roots when needed.
Last updated: August 30, 2026
Frequently asked questions
How do I solve x² − 3x + 2 = 0?
Using the quadratic formula with a=1, b=−3, c=2: the discriminant is 9 − 8 = 1, giving two real roots x = 2 and x = 1.
What does a negative discriminant mean?
A negative discriminant means the equation has no real solutions - the roots are complex numbers, since you'd need the square root of a negative number.
What if a quadratic equation has no real solutions?
That happens when the discriminant (b² − 4ac) is negative - the equation still has two solutions, but they're complex numbers involving the imaginary unit i, since you can't take the square root of a negative number within the real numbers.
What's the difference between the quadratic formula and factoring?
Factoring only works cleanly when a quadratic has simple, often whole-number roots; the quadratic formula always works, for any quadratic equation, whether the roots are whole numbers, fractions, decimals, or complex numbers. This calculator uses the formula directly, so it handles every case without needing to guess factors first.
Is a 'quadratic equation formula calculator,' 'solve quadratic formula calculator,' and 'calculator for solving quadratic equations' the same as this tool?
Yes - every one of these names describes solving ax² + bx + c = 0 for x, which is exactly what this calculator does. Enter your a, b, and c coefficients above and it applies the quadratic formula automatically, real or complex roots included.
Does this show the steps, like a 'math solver with steps'?
Yes - scroll the table below the result for the full step-by-step work: identifying a, b, c, computing the discriminant, taking the square root, and solving for x.