Calculator Input
Use the mode selector below. The inputs follow a three-column layout on large screens, two-column on smaller screens, and one-column on mobile.
Example Data Table
| Mode | Input Example | Worked Output | Graph Meaning |
|---|---|---|---|
| Linear | 2x + 5 = 17 | x = 6 | Intersection of 2x + 5 and 17 |
| Quadratic | x² - 5x + 6 = 0 | x = 2, x = 3 | Parabola crossing the x-axis twice |
| Expression | 2x² + 3x - 4, x = 2 | y = 10 | Curve with highlighted evaluated point |
Formula Used
Linear equations: Rearranging ax + b = c gives x = (c - b) / a when a ≠ 0.
Quadratic equations: For ax² + bx + c = 0, the quadratic formula is x = (-b ± √(b² - 4ac)) / 2a.
Discriminant: D = b² - 4ac. If D is positive, roots are real and distinct. If zero, one repeated root exists. If negative, roots are complex.
Expression evaluation: Replace x with the chosen value, then follow operator order to compute the result.
Graphing: The graph plots the solved line, the parabola, or the expression curve. Highlighted points show roots, intersections, vertices, or selected substitutions.
How to Use This Calculator
- Choose the solving mode from the dropdown.
- Enter the values for your equation or expression.
- Press Show Result to calculate instantly.
- Read the worked steps shown above the form.
- Review the summary table for important values.
- Study the Plotly graph to understand the algebra visually.
- Use the CSV button for tabular exports.
- Use the PDF button to save the worked result.
Frequently Asked Questions
1. What can this algebra calculator solve?
It solves linear equations, quadratic equations, and algebraic expressions with substitution. It also shows working steps, summary values, and a graph for better understanding.
2. Does it really show the full working?
Yes. Each mode lists the solving process step by step. That makes it easier to follow the algebra, verify the answer, and use the method for homework practice.
3. What input format should I use for expressions?
Use numbers, x, parentheses, and operators such as +, -, *, /, and ^. You can type expressions like 2x^2+3x-4 or 3(x+2).
4. What does the graph show for each mode?
For linear mode, it shows the intersection between both sides. For quadratic mode, it shows the parabola. For expression mode, it plots the curve and highlights the selected evaluated point.
5. Why is the discriminant important?
The discriminant tells you the nature of quadratic roots. Positive means two real roots. Zero means one repeated root. Negative means two complex roots.
6. Can I export the result?
Yes. Use the CSV button to download the steps and values in spreadsheet form. Use the PDF button to save the visible result area as a report.
7. What happens if a linear equation has no solution?
The calculator identifies inconsistent equations and reports no solution. It also detects identity equations, where infinitely many x values satisfy both sides.
8. Is this calculator useful for students and teachers?
Yes. Students can learn from the shown steps, while teachers can use the worked examples, graph visuals, and export features for quick demonstrations.