Equation Solver
Solve any math equation with step-by-step solutions. Supports linear, quadratic, polynomial, rational, exponential, and trigonometric equations.
Formula:ax + b = c → x = (c-b)/a
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f(x)
Equation Solving Practice
Test your skills with practice problems
Practice with 5 problems to test your understanding.
What is an Equation?
An equation is a mathematical statement that asserts the equality of two expressions. Solving an equation means finding all values of the unknown variable(s) that make the equation true. These values are called solutions or roots of the equation.
An equation solver finds the values of unknown variables that make an equation true. Use our free calculator to solve any equation instantly with step-by-step solutions. Simply enter your equation like 2x + 5 = 11 or x^2 - 4 = 0 and get the solution with detailed explanations.
Key Facts About Equations
- •Linear equations (ax + b = c) have exactly one solution
- •Quadratic equations (ax² + bx + c = 0) have up to two solutions
- •The discriminant (b² - 4ac) determines the number of quadratic solutions
- •Polynomial equations of degree n have at most n real solutions
- •Some equations have no real solutions (only complex solutions)
- •Always check your solution by substituting back into the original equation
- •Equations can be transformed by performing the same operation on both sides
- •Division by zero is undefined - check for restrictions on the variable
Frequently Asked Questions
How do I solve for x?
Enter your equation with an equals sign (=) and the variable x. The solver will find all values of x that satisfy the equation. For example, enter "2x + 5 = 11" to find that x = 3.
What types of equations can this solve?
This solver handles linear equations (like 2x + 5 = 11), quadratic equations (like x² - 4 = 0), polynomial equations, rational equations with fractions, exponential equations (like 2^x = 8), and basic trigonometric equations.
Why does my equation have no solution?
Some equations have no real solutions. For example, x² = -1 has no real solutions because no real number squared gives a negative result. The equation might have complex (imaginary) solutions instead.
How do I enter fractions and exponents?
Use / for fractions (e.g., x/2 for x divided by 2) and ^ for exponents (e.g., x^2 for x squared). You can also use sqrt(x) for square root and parentheses for grouping.
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).