Calculator Inputs
Choose a solver mode. Inputs use a responsive 3-column, 2-column, and 1-column layout by screen size.
Example Data Table
| Example Type | Sample Inputs | Expected Output |
|---|---|---|
| Linear | a = 4, b = -20 | x = 5 |
| Quadratic | a = 1, b = -5, c = 6 | x₁ = 3, x₂ = 2 |
| Quadratic | a = 1, b = 2, c = 5 | x₁ = -1 + 2i, x₂ = -1 - 2i |
| Simultaneous 2×2 | a₁ = 2, b₁ = 3, c₁ = 13; a₂ = 1, b₂ = -1, c₂ = 1 | x = 3.2, y = 2.2 |
Formula Used
1) Linear Equation
For ax + b = 0, the solution is x = -b / a, when a is not zero. If a = 0, the equation may have no solution or infinite solutions.
2) Quadratic Equation
For ax² + bx + c = 0, the discriminant is Δ = b² - 4ac. The roots are x = (-b ± √Δ) / 2a. The graph also shows the vertex at x = -b / 2a.
3) Simultaneous 2×2 Equations
For a₁x + b₁y = c₁ and a₂x + b₂y = c₂, use Cramer's Rule. D = a₁b₂ - a₂b₁, Dₓ = c₁b₂ - c₂b₁, Dᵧ = a₁c₂ - a₂c₁, then x = Dₓ / D and y = Dᵧ / D.
How to Use This Calculator
- Select the equation type from the dropdown menu.
- Enter the required coefficients for that solver mode.
- Click Solve Equation to calculate the answer.
- Review the result panel shown above the form.
- Check the worked steps, summary table, and graph.
- Use the CSV or PDF buttons to save the result.
Frequently Asked Questions
1) What equation types does this calculator solve?
It solves linear equations, quadratic equations, and simultaneous 2×2 systems. Each mode uses its own input fields, formulas, summary table, and graph.
2) Can it show complex roots?
Yes. When a quadratic equation has a negative discriminant, the calculator returns complex conjugate roots and still plots the parabola on the real plane.
3) Why does a linear equation sometimes show no solution?
If the x coefficient is zero and the constant is not zero, the statement becomes impossible. An example is 0x + 5 = 0, which has no solution.
4) What does determinant mean in simultaneous equations?
The determinant measures whether the two equations have a unique intersection. A nonzero determinant gives one solution. A zero determinant means the system is dependent or inconsistent.
5) What does the graph show for each solver?
Linear mode shows the line and root. Quadratic mode shows the parabola, roots when real, and vertex. Simultaneous mode shows both lines and the intersection point when one exists.
6) Can I export my result?
Yes. The CSV button exports the result summary table. The PDF button saves the visible result area, including steps and graph, as a PDF file.
7) Is this suitable for study and homework checking?
Yes. It provides worked steps, equation status, and graph output. That makes it useful for revision, checking answers, and explaining algebraic results clearly.
8) What happens if a quadratic coefficient equals zero?
The calculator automatically treats the expression as a reduced linear case. It explains that the x² term vanished and then solves the remaining equation.