Quadratic equation solver
Solve ax² + bx + c = 0 for its roots, vertex, intercepts and factored form.
Quadratic equation solver
Enter the coefficients of a quadratic equation — a, b and c in ax² + bx + c = 0 — or paste the equation itself, and this tool solves it instantly. It calculates the discriminant, both roots (real or complex), the vertex of the parabola, where it crosses the x- and y-axes, and its factored form, all updating live as you type.
Switch "Input as" between coefficients and a written equation. Coefficients accept "a=1 b=-3 c=2" or a bare "1,-3,2" per line. Equation mode reads standard notation like "x^2 - 3x + 2 = 0" or "2x² + 5x = 3 - x", moving everything to one side automatically. "Root form" chooses between exact roots — a reduced fraction with a simplified square root, such as "1 + √2" — and rounded decimals, with "Decimal places" controlling the precision. Turn on "Show calculation steps" to see the discriminant and quadratic formula worked out line by line, and toggle the vertex/axis and factored-form sections on or off independently.
When the discriminant is negative the roots are a complex conjugate pair, shown as "p ± qi" — the tool never hides this behind a rounding error, and the factored-form and x-intercept lines say plainly that there is no real factorization in that case. Paste multiple equations, one per line, to solve a whole batch at once; a bad line is reported inline without breaking the rest of the list, and the tally above the output counts how many were real versus complex.
Everything runs locally in your browser — no coefficient or equation you type is ever uploaded anywhere. Copy the result, download it as a .txt file, or send the output back into the input to keep working on it.