What types of equations can this solver handle?

This solver handles linear equations (degree 1), quadratic equations (degree 2), cubic equations (degree 3), and general polynomial equations in one variable.

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.

Quadratic Formula Calculator — Step-by-Step Linear, Quadratic & Polynomial

How the Quadratic Formula Calculator 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 calculator solves standard quadratic equations in the form ax² + bx + c = 0, including equations with positive and negative coefficients, irrational roots, repeated roots, and non-factorable expressions. The solver automatically detects the equation structure, extracts coefficients, calculates the discriminant, and applies the most appropriate solving method.

Enter equations using standard algebra notation such as x^2 - 5x + 6 = 0 or 2x^2 + 3x = 7. Use the ^ symbol for powers. The calculator automatically rearranges equations into standard quadratic form before solving and graphing the parabola.

The solver calculates the discriminant using b² − 4ac before solving the equation. A positive discriminant produces two distinct real roots, a discriminant of zero produces one repeated root, and a negative discriminant indicates complex roots. The calculator explains this process step by step in the diagnostics and solution breakdown.

Yes. Every solution includes coefficient extraction, discriminant analysis, substitution into the quadratic formula, simplification of radicals where possible, verification of roots, and graph visualization. This makes the calculator useful for learning, homework checking, revision, and exam preparation.

Yes. The calculator includes a PDF export feature that generates a clean printable report containing the equation, discriminant analysis, step-by-step solution, diagnostics, verification results, and parabola graph. The exported layout is optimized for readability and academic use.

If the discriminant is negative, the equation has no real x-intercepts. The calculator automatically detects this condition, explains why the parabola does not cross the x-axis, and displays the discriminant analysis clearly in the diagnostics section.

Yes. The graph automatically plots the parabola, roots, y-intercept, and vertex whenever they fall within the visible graph range. This helps visualize how the quadratic function behaves and how the discriminant affects the number and position of the roots.