Equation Solver
Solve linear equations, quadratic equations, and systems of two equations with this equation solver. Step-by-step solutions included.
About Equation Solver
This equation solver handles the three most common equation types you encounter in algebra and precalculus. Select the equation type, enter your coefficients, and get an instant solution with full working shown.
Linear Equations
For equations in the form ax + b = c, enter the three values and the solver isolates x step by step. It handles edge cases like a = 0 where there may be no solution or infinitely many solutions.
Quadratic Equations
For ax² + bx + c = 0, the solver applies the quadratic formula, computing the discriminant to determine whether the roots are real or complex. The result includes both roots and the discriminant value with a badge indicating the root type. For a dedicated quadratic tool with parabola graphing, try the Quadratic Formula Calculator.
Systems of Two Linear Equations
Enter the coefficients for two equations with variables x and y. The solver uses Cramer's rule to find the unique intersection point, or identifies when the lines are parallel (no solution) or coincident (infinitely many solutions). A verification step confirms the answer is correct.
Privacy
All solving happens in your browser. Nothing is sent to any server. For more complex fraction arithmetic, the Fraction Calculator pairs well with this tool.
Frequently Asked Questions
What types of equations can this solve?
This tool handles three types: linear equations in the form ax + b = c, quadratic equations in the form ax² + bx + c = 0, and systems of two linear equations with two variables (a₁x + b₁y = c₁ and a₂x + b₂y = c₂).
How does it solve systems of two equations?
It uses Cramer's rule, which calculates the determinant of the coefficient matrix and then finds x and y by dividing related determinants. If the main determinant is zero, the system either has no solution (parallel lines) or infinitely many solutions (same line).
What happens when an equation has no solution?
The solver clearly tells you when no solution exists. For linear equations this happens when the x coefficient is zero but the equation is inconsistent. For systems, it happens when the lines are parallel. For quadratic equations, you may get complex roots instead.
Does it show the work?
Yes. Every solution includes a numbered step-by-step walkthrough showing each algebraic operation, from writing the initial equation through to the final answer.
Can I enter decimal or negative coefficients?
Yes. All inputs accept any real number, including decimals and negative values. The step-by-step solution handles these correctly throughout the computation.