| Equation Type |
Sample Input |
Expected Main Result |
| Linear |
2x + 4 = 10 |
x = 3 |
| Quadratic |
x² - 5x + 6 = 0 |
x = 2, 3 |
| Cubic |
x³ - 6x² + 11x - 6 = 0 |
x = 1, 2, 3 |
| System |
2x + 3y = 13, x - y = 1 |
x = 3.2, y = 2.2 |
| Absolute |
|2x - 6| = 8 |
x = 7, -1 |
Linear: For ax + b = c, use x = (c - b) / a.
Quadratic: For ax² + bx + c = 0, use D = b² - 4ac and x = (-b ± √D) / 2a.
Cubic: The calculator normalizes the equation and applies Cardano based steps.
System: Cramer's Rule uses D = a₁b₂ - a₂b₁, x = Dx / D, and y = Dy / D.
Exponential: For a × b^(kx) + c = d, use x = ln((d - c) / a) / (k ln b).
Logarithmic: Convert the log equation into exponential form, then isolate x.
How to Use This Calculator
- Select the equation type from the dropdown menu.
- Enter each coefficient in the matching input box.
- Use negative numbers where the equation has subtraction.
- Press the calculate button to view the answer and work.
- Read the domain notes for rational, exponential, and log equations.
- Download the result as a CSV file or PDF document.
Why Showing Work Matters
An equation calculator is most useful when it explains each move. A final answer alone can hide important logic. This tool displays the selected model, the substitution, the transformed equation, and the final value. That makes the result easier to check. It also helps students find mistakes in signs, exponents, and copied coefficients.
Supported Algebra Patterns
The page supports common algebra patterns. Linear equations use inverse operations. Quadratic equations use the discriminant and the quadratic formula. Cubic equations are normalized before Cardano steps are applied. Systems use determinants, so dependent or inconsistent lines can be detected. Other modes cover proportions, absolute values, rational forms, exponential expressions, and logarithmic equations.
Better Study Records
Showing work builds confidence. A learner can compare each step with class notes. A teacher can use the exported result as a quick review record. The CSV file is useful for spreadsheets. The document export is helpful for worksheets or saved solution logs. Each mode also gives reminders about restrictions, such as nonzero denominators and positive log bases.
Input Accuracy
Accuracy still depends on input quality. Enter coefficients exactly as they appear in the problem. Use negative signs where needed. Avoid rounding until the end when possible. For word problems, translate the situation into a supported equation first. Then read the steps before trusting the answer. If a denominator, base, or coefficient breaks a rule, the calculator explains why no real solution is returned.
Learning Value
This kind of tool should not replace learning. It should support it. Try solving the problem by hand first. Then use the calculator to confirm your result. When the answer differs, compare every displayed step. The difference often reveals a missed sign, a wrong operation, or a hidden domain condition. Over time, that habit improves algebra speed and accuracy.
Export Benefits
Good equation practice also needs clear records. The result panel lists values in a compact table. It keeps the steps in order, so revision stays simple. You can test several examples and export each answer. This helps when preparing notes, comparing methods, or checking homework sets. The calculator gives decimal results with sensible precision, while still showing the exact formula used. It is designed for quick review and careful algebra practice anytime online.
1. What equations can this calculator solve?
It solves linear, quadratic, cubic, system, proportion, absolute value, rational, exponential, and logarithmic equations. Each mode has its own fields and step-by-step explanation.
2. Does it show every step?
Yes. The result panel shows the main transformations, formula substitution, domain checks, and final answer. Some long methods are summarized for readability.
3. Can I download the result?
Yes. After calculation, you can download the solution table as a CSV file. You can also save the answer and worked steps as a PDF document.
4. Why does the calculator reject some answers?
Some equations have domain rules. Rational equations cannot divide by zero. Log inputs must be positive. Exponential log transformations need positive values.
5. Can it solve complex roots?
Yes. Quadratic and cubic modes can display complex roots when the equation requires them. Real roots are also shown where available.
6. What should I enter for missing terms?
Enter zero for any missing coefficient. For example, use b = 0 when a quadratic has no x term. This keeps the formula correct.
7. Is this useful for homework checking?
Yes. It is useful for checking algebra work, reviewing formulas, and comparing manual answers. You should still understand each displayed step.
8. Why are decimal answers rounded?
The calculator formats long decimals for readability. The internal calculations use numeric precision, then display sensible rounded values in the result table.