Math Solver

Quadratic Solver

Solve any quadratic equation in standard form with real or complex roots, discriminant analysis, vertex details, and a live parabola graph. The full work stays visible so it still helps when you need to learn the process, not just the answer.

Step-by-step work See the discriminant, quadratic formula substitution, and simplified roots laid out in order.

Complex roots supported Negative discriminant cases show the imaginary part cleanly instead of erroring out.

Visual graph The SVG graph redraws for each equation and marks the vertex and real intercepts when they exist.

Equation Inputs

Enter coefficients for ax² + bx + c = 0. The leading coefficient `a` cannot be zero or the equation is not quadratic.

a b c

Ready. Enter coefficients and click Solve Equation.

Equation

x² - 5x + 6 = 0

Discriminant

Root Type

Two real roots

Axis of Symmetry

x = 2.5

Vertex

(2.5, -0.25)

Y Intercept

(0, 6)

Parabola Graph

The graph auto-centers around the vertex and any real roots so you can see the curve shape immediately.

Parabola

Vertex