Quadratic Equation Solver — roots & vertex
Solve ax²+bx+c=0 for real or complex roots, with the discriminant, vertex and axis of symmetry.
🔒 Runs entirely in your browser. Your input and output are never sent to a server or stored — fully private.
a·x² + b·x + c = 0
Roots update live as you type. Complex roots are shown as p ± qi. Click any result to copy.
About this tool
This quadratic equation solver takes the coefficients a, b and c from ax²+bx+c=0 and finds the roots using the quadratic formula, whether they are real or complex. Alongside the solutions it reports the discriminant, the coordinates of the parabola's vertex and its axis of symmetry, so you see the full picture of the equation. The work is done instantly in your browser.
Frequently asked questions
What does the discriminant tell me?
The discriminant is the value b²-4ac under the square root in the quadratic formula, and its sign tells you the nature of the roots. A positive discriminant gives two distinct real roots, zero gives a single repeated root, and a negative value means the two roots are complex.
Can it solve equations with no real solutions?
Yes. When the discriminant is negative there are no real roots, and the solver returns the pair of complex conjugate solutions in a + bi form instead of leaving the answer blank.
Is my data sent anywhere?
No. The equation is solved entirely in your browser, so the coefficients you enter are never sent to or stored on a server.