Equation Solver — Step-by-Step Working
Solve linear, quadratic, and simultaneous equations with every algebraic step shown. Enter coefficients, click Solve, and follow the working from the starting equation to the final answer. No signup, runs entirely in your browser.
Algebra Tips
Check with substitution
After solving, substitute your answer back into the original equation to verify. For x = 4 in 2x + 3 = 11: 2(4) + 3 = 11. If both sides match, the solution is correct.
Negative coefficients
Enter negative values directly: use -3 for a = -3. The solver handles negative coefficients correctly for all three equation types.
Discriminant insight
Before solving a quadratic, calculate b² − 4ac mentally. If negative, no real solutions. If zero, one solution. If positive, two solutions. This check takes 10 seconds and saves time on exams.
Simultaneous equations
For the system solver, rearrange your equations into ax + by = c form before entering the coefficients. Mixed signs (e.g. x − 2y = 3) enter as a=1, b=-2, c=3.
Frequently Asked Questions
What types of equations can it solve?
Linear equations (ax + b = c), quadratic equations (ax² + bx + c = 0), and systems of two linear equations (ax + by = c and dx + ey = f). All three types show complete step-by-step working.
How does it solve linear equations?
For ax + b = c, the solver first subtracts b from both sides to isolate the x term, then divides by a to find x. Each step is shown with the resulting equation.
What is the quadratic formula?
For ax² + bx + c = 0, the formula is x = (−b ± √(b² − 4ac)) / 2a. The discriminant (b² − 4ac) determines the number of solutions: positive = two real solutions, zero = one repeated solution, negative = two complex solutions.
What is Cramer's rule?
Cramer's rule solves a 2×2 system by computing determinants. For a₁x + b₁y = c₁ and a₂x + b₂y = c₂, the solution is x = (c₁b₂ − c₂b₁) / (a₁b₂ − a₂b₁) and y = (a₁c₂ − a₂c₁) / (a₁b₂ − a₂b₁). If the denominator is 0, there is no unique solution.
What does a negative discriminant mean?
A negative discriminant means the quadratic has no real solutions — the parabola does not intersect the x-axis. The complex solutions are shown in the form a ± bi where i = √(-1).
Is my data stored?
No. All solving runs locally in your browser. No data is sent to any server.