Quadratic Formula Calculator
Free, with no sign up. Calculations run on your device; your entries stay in this browser.
Each coefficient must be zero or have magnitude from 10⁻¹² to 10¹². Floating-point roots are approximate; results show 14 significant digits. A positive discriminant gives two real roots, zero gives one repeated root and a negative discriminant gives a conjugate complex pair. If a is zero, the equation is linear or constant. Coefficients and x use your consistent algebraic units.
Your result
D = b² − 4ac; x = (−b ± √D)/(2a). For D < 0, real part = −b/(2a), imaginary magnitude = √(−D)/(2|a|). Real roots use q = −(b + sign(b)√D)/2, then q/a and c/q to reduce cancellation (sign(0) = 1). When a = 0, bx + c = 0.
Primary source: OpenStax, quadratic functions and formula.
Worked example
x² − 3x + 2 = 0 has D = 9 − 8 = 1, so x = 1 or 2. x² + 1 = 0 has roots +i and −i.
How to use this tool
Enter a, b and c in ax² + bx + c = 0, then select Calculate.
Frequently asked questions
What if a is zero?
A nonzero b gives the linear root −c/b. If a and b are both zero, c = 0 is an identity and any x works; otherwise there is no solution.
How are complex roots shown?
A negative discriminant gives two conjugate roots as real part plus or minus an imaginary part followed by i.
Is this free and private?
Yes. These calculations run in your browser, without sign-up or uploading your entries.