Math Tools
Educational Tools
Web UtilitiesEquation Solver
Solve linear, quadratic, cubic, and quartic equations instantly with step-by-step solutions.
Enter Your Equation
Use x as the variable. For powers, use ^ (e.g., x^2, x^3, x^4). Solution updates automatically.
Example Equations:
Solution
Enter an equation to see the solution instantly.
Supports linear, quadratic, cubic, and quartic equations
Understanding Equation Types
Linear Equations (ax + b = c)
Linear equations have the variable to the first power. The general form is ax + b = c.
Example: 2x + 5 = 13
Solution: x = 4
Method: Isolate x by algebraic manipulation
Quadratic Equations (ax² + bx + c = 0)
Quadratic equations have the variable squared, solved using the quadratic formula.
Example: x² - 5x + 6 = 0
Solutions: x₁ = 3, x₂ = 2
Formula: x = (-b ± √(b² - 4ac)) / (2a)
Cubic Equations (ax³ + bx² + cx + d = 0)
Cubic equations have the variable to the third power, solved using Cardano's formula.
Example: x³ - 6x² + 11x - 6 = 0
Solutions: x = 1, 2, 3
Method: Cardano's formula with trigonometric solution
Quartic Equations (ax⁴ + bx³ + cx² + dx + e = 0)
Quartic equations have the variable to the fourth power, solved using Ferrari's method.
Example: x⁴ - 5x² + 4 = 0
Solutions: x = ±1, ±2
Method: Ferrari's formula via resolvent cubic
Tips for Using the Equation Solver
- Always write your equation with an equals sign (=)
- Use x as your variable (lowercase)
- For powers, use ^ notation: x^2 for x², x^3 for x³, x^4 for x⁴
- Decimal coefficients are supported (e.g., 2.5x + 3.7 = 10)
- Solutions appear automatically as you type (with a short delay)
- The solver handles linear, quadratic, cubic, and quartic equations
- Step-by-step solutions help you understand the solving process
- Complex solutions are displayed when equations have no real solutions
- Try the example equations to see how different types are solved
- Cubic and quartic solutions use advanced mathematical formulas (Cardano, Ferrari)
Related Tools
About Equation Solver
How It Works
- Parses equations in standard mathematical notation
- Automatically detects equation type (linear, quadratic, cubic, quartic)
- Applies appropriate solving algorithm
- Shows step-by-step solution process
- Handles real and complex solutions
- Auto-solves as you type with smart debouncing
- Provides detailed explanations for learning
Common Use Cases
- Homework help and verification
- Learning algebra and polynomial equations
- Physics and engineering calculations
- Mathematical modeling and analysis
- Test preparation and practice
- Quick equation solving for professionals
- Advanced mathematics (cubic/quartic equations)
Frequently Asked Questions
What types of equations can this solver handle?
This equation solver can handle linear equations (ax + b = c), quadratic equations (ax² + bx + c = 0), and cubic equations (ax³ + bx² + cx + d = 0). It provides step-by-step solutions for all supported equation types with detailed explanations of the solving process.
How do I input an equation?
Enter your equation in standard form with the variable x. For linear equations, use the form "ax + b = c". For quadratic equations, use "ax² + bx + c = 0". For cubic equations, use "ax³ + bx² + cx + d = 0". Use "x^2" or "x²" for squared terms and "x^3" or "x³" for cubic terms.
Does the solver show the steps to solve the equation?
Yes! The solver provides detailed step-by-step solutions showing exactly how the equation is solved. This includes showing the formula used, intermediate calculations, and the final answer, making it an excellent learning tool for students.
Can it solve quadratic equations with complex or imaginary solutions?
Yes, the quadratic equation solver can handle equations with complex solutions. When the discriminant (b² - 4ac) is negative, the solver will display the complex solutions in the form a + bi, where i is the imaginary unit.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to solve equations of the form ax² + bx + c = 0. It works for all quadratic equations and provides both real and complex solutions. The solver displays this formula and shows how it's applied to your specific equation.
How do I solve a simple linear equation like 2x + 5 = 13?
Enter the equation "2x + 5 = 13" into the solver. It will isolate x by subtracting 5 from both sides (2x = 8) and then dividing both sides by 2 (x = 4). The solver shows each step clearly.
What does the discriminant tell me about a quadratic equation?
The discriminant (b² - 4ac) determines the nature of the solutions: If positive, there are two distinct real solutions. If zero, there is one repeated real solution. If negative, there are two complex conjugate solutions. The solver calculates and displays the discriminant value.
Can I solve equations with fractions or decimals?
Yes, the equation solver accepts decimal numbers and can handle equations with fractional coefficients. Enter decimals directly (like 2.5x + 3.7 = 10.2) and the solver will calculate precise solutions.
What if my equation has no solution or infinite solutions?
For linear equations, if the coefficients result in 0 = 0, there are infinite solutions. If they result in a contradiction like 0 = 5, there is no solution. The solver will detect and clearly indicate these special cases.
How accurate are the solutions?
The solver uses precise mathematical calculations and displays results with appropriate decimal precision. For irrational solutions (like those involving square roots), results are shown to several decimal places while also displaying the exact radical form when applicable.
Can this help me learn algebra?
Absolutely! The step-by-step solutions make this tool excellent for learning. You can see exactly how each equation is solved, understand the formulas applied, and verify your homework. It's designed to be educational, not just a calculator.
What are some real-world applications of solving equations?
Equation solving is used in physics for motion and energy calculations, engineering for structural analysis, finance for interest and investment calculations, chemistry for reaction rates, computer science for algorithm optimization, and many other fields that require mathematical modeling and problem-solving.