Equation Solver
Linear, quadratic and 2-variable equations — with steps
x =
D = b² − 4ac = —
x₁ = , x₂ =
x =
x = ± i
x = , y =
No unique solution — the equations are parallel/dependent
Equation Solver — Complete Guide & Instructions
MakeCard Equation Solver handles the three equation types students meet most: single linear equations, quadratics, and two-variable simultaneous systems. Enter the coefficients in the on-screen equation layout and the answer appears with working — including the discriminant for quadratics and complex roots when they occur. It is a fast check for algebra homework and everyday equation problems.
How to Use Equation Solver
- 1 Choose the mode: Linear, Quadratic, or 2-Variable.
- 2 Fill the coefficient boxes in the displayed equation (ax + b = c, ax² + bx + c = 0, or the pair).
- 3 The solution appears automatically — linear shows step-by-step working.
- 4 For quadratics, read the discriminant and both roots (or the complex pair).
Key Features & Capabilities
- Three solvers in one: linear ax + b = c, quadratic ax² + bx + c = 0, and 2×2 systems.
- Step-by-step working shown for linear equations.
- Discriminant (b² − 4ac) computed and explained for quadratics.
- Handles real, repeated, and complex roots.
- Detects parallel/dependent systems with no unique solution.
- Negative and decimal coefficients fully supported.
Supported Formats & Specifications
| Parameter | Specification |
|---|---|
| Modes | Linear (1 variable), quadratic (x²), simultaneous (x and y) |
| Quadratic output | Discriminant, two roots, single root, or complex pair |
| System output | x and y values, or no-unique-solution notice |
Practical Everyday Use Cases
- Checking algebra homework for class 8–12 equations.
- Solving price-quantity problems that reduce to two equations.
- Verifying quadratic roots before plotting or further work.
- Quick answers to everyday "solve for x" puzzles.
Pro Tips for Best Results
- Rearrange your equation to standard form first — all terms on the left for quadratics.
- A negative discriminant means no real roots; the tool shows the complex pair instead.
- For 2-variable mode, write both equations as ax + by = c before entering coefficients.
Common Problems & Solutions
The two equations are parallel or dependent — check the coefficients; if one equation is a multiple of the other, infinite solutions exist.
Sign errors are the usual cause — a coefficient entered as positive instead of negative flips the whole result.
Privacy & Security
100% Client-Side Execution
Coefficients are solved in your browser only — no equations are transmitted or stored.
Frequently Asked Questions
Everything you need to know about using Equation Solver
Enter a, b, and c in Quadratic mode — the tool computes the discriminant and both roots instantly, including complex roots when the discriminant is negative.
b² − 4ac. Positive means two real roots, zero means one repeated root, and negative means two complex roots — the solver labels each case.
Yes — the 2-Variable mode solves simultaneous equations of the form ax + by = c and returns both x and y.
Enter the three numbers in Linear mode — the working shows x = (c − b) ÷ a step by step.
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