What types of equations can this solver handle?

This solver handles linear, quadratic, cubic, polynomial (up to degree 5), trigonometric, exponential, logarithmic, rational, absolute value, radical, diophantine, and recurrence equations. It also solves systems of linear and non-linear equations, ODEs, modular arithmetic, and inequalities.

Does the equation solver show step-by-step solutions?

Yes, every solution includes detailed step-by-step working. The solver uses methods like the quadratic formula, Gaussian elimination, Newton-Raphson, and symbolic techniques to show exactly how the answer is derived.

Can it solve non-linear systems of equations?

Yes. The solver automatically detects whether a system is linear or non-linear. Linear systems use Gaussian elimination, while non-linear systems are solved using the Newton-Raphson method with multiple initial guesses to find all solutions.

Is this equation solver free to use?

Yes, this equation solver is completely free. No sign-up or payment is required. All calculations run directly in your browser.

Equation Solver — Solve Any Equation Step-by-Step

Equation

Supports: +, -, *, /, ^, sqrt(), sin(), cos(), tan(), log(), exp(), abs(), pi, e
Use = to define the equation. Variable: x

Examples

2x + 5 = 13 x² - 5x + 6 = 0 x³ - 6x² + 11x - 6 = 0 sin(x) = 0.5 eˣ = 10 log(x) = 2 2^x = 16 √x + 3 = 7 |x - 3| = 5 x⁴ - 10x² + 9 = 0

System of Equations

Supported variables: x, y, z, w. Use = in each equation.
Supports both linear and non-linear systems (e.g., x² + y² = 25).

Examples

2×2 linear 3×3 linear 3×3 mixed non-linear circle non-linear pair product & sum

Polynomial Degree

Coefficients

Examples

x² - 5x + 6 x² - 4 x³ - 6x² + 11x - 6 x⁴ - 10x² + 9

Trigonometric Equation

Functions: sin, cos, tan, cot, sec, csc, asin, acos, atan
Finds all solutions in a range and the general formula.

Range Min (radians)

Range Max (radians)

Examples

sin(x) = 1/2 cos(x) = -1 tan(x) = 1 2sin²(x) - 1 = 0 sin(2x) = cos(x) cos²(x) - sin(x) = 0

Rational Equation

Equations with fractions involving x. Automatically checks for excluded values (division by zero).

Examples

(x+1)/(x-2) = 3 1/x + 1/(x+1) = 5/6 2x/(x-1) - 3/(x+2) = 1 x/(x-3) = 9/(x²-9)+1 (x²-1)/(x+1) = 2

ODE Type

Examples

Modular Equation Type

Examples

Inequality

Supports: >, <, >=, <=. Solves linear and quadratic inequalities.

Examples

2x + 3 > 7 3x - 5 ≤ 10 x² - 4 < 0 x² - 5x + 6 ≥ 0

Exponential Equation

Equations with variables in exponents. Uses logarithms for step-by-step solutions.
Supports: a^x, e^x, exp(x)

Examples

2ˣ = 16 eˣ = 10 3²ˣ = 81 5^(x-1) = 125 2ˣ + 2ˣ⁺¹ = 24 e²ˣ - 5eˣ + 6 = 0

Logarithmic Equation

log() = natural log (ln), log10() = base 10, log2() = base 2.
Domain: arguments of log must be positive.

Examples

log₁₀(x) = 2 ln(x) = 3 ln(x)+ln(x-3) = ln(10) 2·ln(x) = ln(25) log₁₀(x²-1) = 1

Absolute Value Equation

Use abs() for absolute value. Solves by case analysis.
|f(x)| = g(x) splits into: f(x) = g(x) or f(x) = −g(x)

Examples

|2x - 3| = 7 |x+1| = |x-3| |x²-4| = 3 |x| = 2x - 1 |3x+2|+|x-1| = 7

Radical Equation

Equations with square roots or cube roots. Checks for extraneous solutions.
Supports: sqrt(), cbrt(), x^(1/n)

Examples

√(x+3) = 5 √(2x-1) = x-2 √x + √(x+5) = 5 ∛(x-1) = 2 √(x+7) - √x = 1

Linear Diophantine Equation

Form: ax + by = c (integer solutions only)

Finds all integer solutions using the Extended Euclidean Algorithm.
Solutions exist iff gcd(a, b) divides c.

Examples

3x + 5y = 1 6x + 10y = 14 12x + 8y = 4 7x + 11y = 1 4x + 6y = 3 (none)

Recurrence Type

Examples

Operation

Examples

Solution

Step-by-Step Solution

JavaScript Required

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This solver supports: linear equations, quadratic equations, polynomial equations, trigonometric equations, exponential equations, logarithmic equations, systems of linear and non-linear equations, rational equations, ODEs, inequalities, absolute value equations, radical equations, diophantine equations, recurrence relations, and calculus operations.

General Equation Solver

System of Equations Solver

Polynomial Equation Solver

Trigonometric Equation Solver

Rational Equation Solver

Ordinary Differential Equation Solver

Modular Arithmetic Solver

Inequality Solver

Exponential Equation Solver

Logarithmic Equation Solver

Absolute Value Equation Solver

Radical Equation Solver

Diophantine Equation Solver

Recurrence Relation Solver

Calculus Solver

Solution

Step-by-Step Solution

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