Real-domain quadratic formula

Quadratic Equation Calculator

Solve a supported one-variable quadratic with the formula route the beta actually verifies—without promising factoring, complex roots, or multiple methods.

Open the quadratic solver Graph a quadratic

The supported quadratic form

A quadratic equation can be rearranged into the form below, with a nonzero value for a. The discriminant determines how many real roots the equation has.

Standard form

ax^2+bx+c=0

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

The current beta uses this route for supported equations and verifies the displayed result over the real numbers.

A concrete example

For x² − 5x + 6 = 0, the coefficients are a = 1, b = −5, and c = 6. The discriminant is 1, so the formula gives the two real roots x = 2 and x = 3.

What is not promised

Complex-number roots when the discriminant is negative.
Factoring, completing the square, or choosing among multiple teaching methods.
Graph-derived root verification.
Higher-degree polynomials or equations with multiple variables.

Separate tools: The browser graph can visualize y = ax² + bx + c. It is intentionally separate from the verified solver and should be treated as a visual aid.

Questions

Quadratic equation FAQ

Which quadratic equations are supported?

The current beta supports typed one-variable degree-two equations over the real numbers when they can be classified and solved with the quadratic formula inside the resource boundary.

What happens when the discriminant is negative?

The current solver domain is real numbers. A negative discriminant has no real roots; this page does not claim complex-number solving.

Does the quadratic solver show factoring or a graph?

No. The verified solver currently promises the quadratic-formula route, not factoring or multiple solution methods. The separate browser graph can visualize an explicit quadratic but does not verify its roots.

Try a typed quadratic

Use the main workspace for a supported equation such as x² − 5x + 6 = 0 and confirm the parsed expression before solving.

Return to the main solver