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FREE ONLINE EQUATION SOLVER
Equation solver for linear, quadratic, cubic, and system problems.
Solve one-variable equations or build a 2–8 variable system of equations. Use coefficients, compare matrix methods, and read the steps behind the answer.ax² + bx + c = 0
EQUATION SOLVER GUIDE
How to choose the right equation-solving workflow
The best equation solver depends on the form of the problem. Start with the degree of the equation or decide whether the problem is a system of simultaneous equations.Linear equation solver
ax + b = 0Use this when the unknown appears only to the first power. The calculator moves the constant term, divides by the x coefficient, and reports whether there is one solution, no solution, or infinitely many solutions.Example: 2x + 8 = 0 gives x = −4.Quadratic equation solver
ax² + bx + c = 0Use this for degree-two equations. The discriminant tells whether the equation has two real roots, one repeated root, or a pair of complex roots.Example: x² − 5x + 6 = 0 gives x = 2 and x = 3.Cubic equation solver
ax³ + bx² + cx + d = 0Use this for degree-three equations when you want real and complex roots directly from coefficients. For degree 4 to 10, open the Polynomial Solver.Example: x³ − 6x² + 11x − 6 = 0 gives roots 1, 2, and 3.System of equations solver
A · x = bBuild a 2–8 variable simultaneous-equations system from coefficients. Compare auto row reduction, Gaussian elimination, Gauss-Jordan RREF, inverse method, and Cramer’s rule where supported.Example: enter each equation row as coefficients followed by the right-side value.MATRIX METHODS FOR SYSTEMS
Solving simultaneous equations from coefficients
For a system of equations, write coefficients in the same variable order on every row. The calculator builds the coefficient matrix A, the unknown vector x, and the right-side vector b.Gaussian elimination
A practical method for simultaneous equations. It converts the augmented matrix to row echelon form, then uses back-substitution to solve the unknowns.
Gauss-Jordan / RREF
Continues row reduction until pivots are easy to read. RREF also helps identify free variables, inconsistent systems, and dependent equations.
Matrix inverse method
Uses x = A⁻¹b for a square system when the coefficient matrix is invertible. It is useful when the same A matrix is reused with different right-side vectors.
Cramer’s rule
Uses determinants and is mainly useful for small square systems. This workspace keeps Cramer’s rule limited to supported sizes.
WORKED EXAMPLE
System of equations example
For 2x + y − z = 8, −3x − y + 2z = −11, and −2x + y + 2z = −3, enter each coefficient row with the constant at the end.[2, 1, −1 | 8]
[−3, −1, 2 | −11]
[−2, 1, 2 | −3]Can this solve engineering equations online?
Yes. It is useful for coefficient-based engineering, algebra, and linear-system workflows. For formulas with units, combine it with the Scientific Calculator or Unit Converter.
When should I use Polynomial Solver instead?
Use Polynomial Solver for degree 4 through 10 roots. This Equation Solver focuses on linear, quadratic, cubic, and square linear systems.
When should I graph the equation?
Use Graphing Calculator when you want to see intercepts, turning points, intersections, or a table of values. Use Equation Solver when you need numeric roots or system values.