How do I enter a quadratic equation?

Type the equation using standard notation. For example: x^2 - 5x + 6 = 0 or 2x^2 + 3x - 2 = 0. The solver automatically detects the degree and applies the correct method.

What is the discriminant?

The discriminant is b² - 4ac for a quadratic ax² + bx + c = 0. If it is positive, the equation has two distinct real roots. If zero, one repeated root. If negative, two complex roots with no real solutions.

Can this solver handle equations not equal to zero?

Yes. You can enter equations like x^2 = 9 or 2x + 3 = 7. The solver rearranges to standard form automatically before solving.

Does the solver show working steps?

Yes. For every equation type, the solver shows the full algebraic working: standard form, discriminant calculation, quadratic formula substitution, factoring steps, and verification by substituting the roots back.

Equation Solver — Step-by-Step Linear, Quadratic & Polynomial

How the Equation Solver Works

Enter any equation in one variable using standard notation. The solver detects the type — linear, quadratic, or cubic — and applies the correct algebraic method. Every solution includes full step-by-step working and a verification check.

Linear equations (degree 1)

Example: 2x + 3 = 7. The solver collects variable terms, moves constants to the other side, then divides by the coefficient to isolate x. Result: x = 2.

Quadratic equations (degree 2)

Example: x² − 5x + 6 = 0. The solver calculates the discriminant Δ = b² − 4ac. If Δ > 0: two distinct real roots. If Δ = 0: one repeated root. If Δ < 0: no real roots. The quadratic formula x = (−b ± √Δ) / 2a is applied and simplified.

Cubic equations (degree 3)

Example: x³ − 6x² + 11x − 6 = 0. The solver attempts factoring using the rational root theorem, then identifies all three roots and verifies each one.

Entering equations

You can enter equations with or without the right-hand side. x^2 - 4 = 0 and x^2 - 4 are both valid — the solver assumes = 0 if no equals sign is present. Use ^ for powers.

Frequently Asked Questions

This solver handles linear equations (degree 1), quadratic equations (degree 2), cubic equations (degree 3), and general polynomial equations in one variable. It returns exact roots with full step-by-step working.

Type using standard notation: x^2 - 5x + 6 = 0 or 2x^2 + 3x - 2 = 0. Use ^ for powers. The solver automatically detects the degree and applies the quadratic formula or factoring.

The discriminant is b² − 4ac for a quadratic ax² + bx + c = 0. If positive: two distinct real roots. If zero: one repeated root. If negative: no real roots (complex only).

Yes. Enter x^2 = 9 or 2x + 3 = 7 directly. The solver rearranges to standard form automatically before solving.

Yes. Every equation type shows full algebraic working: standard form, discriminant calculation, formula substitution, factoring where applicable, and verification by substituting roots back into the original equation.

If the discriminant is negative, the solver shows "No real solution" and explains why using the discriminant value. Complex roots are not displayed but the reason is shown in the diagnostics.