Solve Equations Step by Step
This equation solver works out linear, quadratic, and systems of equations and shows the full working behind every answer. Enter your coefficients and the solution appears instantly, with each move laid out so you can follow the method, not just copy the result.
Switch between the Linear, Quadratic, and System tabs to match the equation you have. It handles fractions, complex roots, and special cases like no solution or infinitely many solutions — useful whether you are a student checking homework, a teacher building examples, or anyone who needs to solve for x without picking up a pencil.
How to Solve an Equation
Pick the equation type
Choose the Linear tab for ax + b = cx + d, Quadratic for ax² + bx + c = 0, or System for two or three equations solved together.
Enter the coefficients
Type the numbers for each coefficient. Decimals are fine, and any field you leave empty is treated as 0. The equation preview updates as you type so you can see exactly what is being solved.
For systems, choose the size
On the System tab, pick 2 vars or 3 vars, then fill in the coefficient for each row. The solver uses Cramer's Rule with determinants to find x, y, and z.
Read the answer and steps
The solution shows up automatically — no button to press. Review the step-by-step breakdown below it, and hit Clear when you want to start a fresh equation.
Features
Three Equation Types
Solve linear equations (ax + b = cx + d), quadratics (ax² + bx + c = 0), and 2×2 or 3×3 systems of linear equations — all in one tool.
Step-by-step Solutions
Every type shows the full working, from identifying coefficients to the final answer, so you can learn the method and check each line.
Instant Results
Solutions calculate live as you type — no button needed — and the equation preview updates in real time to show what is being solved.
Fraction Display
Answers appear as clean fractions when possible (such as 4/3 instead of 1.333…), with the decimal approximation shown alongside.
Special Case Detection
It flags and explains no solution, infinitely many solutions, and complex (no real) roots so unusual results never look like a mistake.
Quadratic Properties
For quadratics you also get the discriminant (Δ) with color coding, the vertex coordinates, and the axis of symmetry.
Frequently Asked Questions
What types of equations can this solver handle?
Three types: linear equations (first degree, one variable), quadratic equations (second degree, one variable), and systems of linear equations with 2 or 3 variables solved at the same time. Each lives on its own tab.
How do I solve a quadratic equation here?
Open the Quadratic tab and enter a, b, and c for ax² + bx + c = 0. The solver applies the quadratic formula x = (−b ± √Δ) / 2a, then shows the roots, the discriminant, the vertex, and the axis of symmetry with each step written out.
What is the discriminant?
The discriminant Δ = b² − 4ac tells you the nature of a quadratic's roots. If Δ > 0 there are two distinct real roots, if Δ = 0 there is one repeated (double) root, and if Δ < 0 there are no real roots — only complex roots, which the solver still reports.
How do I solve a system of equations?
On the System tab, choose 2 vars or 3 vars and enter the coefficients for each row. The tool uses Cramer's Rule — replacing one column of the coefficient matrix with the constants and dividing determinants — to find x, y, and z, with all the determinant steps shown.
When does an equation have no solution or infinitely many?
A linear equation or system has no solution when it is inconsistent (the equations contradict each other), and infinitely many when the equations are dependent. For systems this shows up as a main determinant D = 0; if the variable determinants are also 0 the answer is infinite, otherwise there is no solution. The solver detects and labels both cases.
What happens if I enter a = 0 in the quadratic solver?
With a = 0 the equation is no longer quadratic — it becomes the linear equation bx + c = 0. The solver detects this automatically and solves it as a linear equation instead of returning an error.
Can I enter decimal numbers and does it show the steps?
Yes to both. Every coefficient field accepts decimals, and results are still shown as fractions when a clean fractional form exists. A complete step-by-step solution is displayed for every equation type, automatically and free to use online.
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