Equation Solver

Enter the coefficients of a linear, quadratic or cubic equation, or of a system of two or three linear equations, and get the solution with the steps that lead to it. Quadratics show the discriminant, vertex and complex roots when they occur. Cubics are solved with Cardano’s formula or the trigonometric method, and systems use Cramer’s rule with Gaussian elimination to detect when there is no unique solution.

How to use the Equation Solver

1. Choose the equation type.
2. Enter the coefficients shown in the template (blank fields count as 0).
3. Press Solve.
4. Read the roots and the step-by-step working, then copy them if needed.

Features

• Linear ax + b = c, including no-solution and all-solutions cases
• Quadratic roots (real or complex), discriminant, vertex and axis
• Cubic roots via Cardano or the trigonometric method
• 2×2 and 3×3 systems with Cramer’s rule
• Detects inconsistent and dependent systems

Benefits

• Check algebra homework and see the method, not just the answer
• Handles complex roots that basic calculators skip
• Numerically stable formulas for accurate results

Frequently asked questions

What does the discriminant tell me?

For ax² + bx + c = 0 the discriminant D = b² − 4ac. If D > 0 there are two real roots, if D = 0 one repeated root, and if D < 0 two complex conjugate roots.

How are cubic equations solved?

The cubic is first reduced to the depressed form t³ + pt + q = 0. When it has three real roots the trigonometric method is used; otherwise Cardano’s formula gives the real root and the two complex ones.

What does "no unique solution" mean for a system?

The coefficient determinant is zero. Elimination then shows either a contradiction such as 0 = 3 (no solution) or a redundant equation (infinitely many solutions).

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