Equation Solver — Linear, Systems, Polynomial, Rational, Exponential & Inequalities
Type any equation and this free equation solver finds x instantly — with every step shown, not just the final number. One tool covers linear equations, systems of equations, cubic/quartic polynomial equations, rational equations, exponential and logarithmic equations, and inequalities. No sign-up, no download, runs entirely in your browser.
Step-by-Step Solution
Whether you're checking two-step equation homework, untangling a system of equations for a chemistry problem, or trying to find every real root of a cubic, the AceCalculator equation solver gives you an answer you can trust — and shows you exactly how it got there.
Type the equation the way you'd write it by hand, press Solve, and the calculator walks through the same moves you'd use on paper: isolating the variable, eliminating a second equation, or scanning for sign changes to pin down every real root of a polynomial. Six modes live in one tool, so you're not bookmarking six different pages for six different equation types.
What You Can Do With This Equation Solver
Linear Equation Solver
The linear equation calculator mode solves for x in one-step, two-step equations, or equations with the variable on both sides — showing each move as it isolates x.
- One-step and two-step equations
- Variable on both sides of the equals sign
- Fractions and decimals handled automatically
System Of Equations Solver
Need to solve for more than one variable at once? The system of equations calculator mode solves two or three simultaneous linear equations using elimination, giving every variable's value in one pass.
- 2-variable and 3-variable systems
- Elimination method shown step by step
- Flags systems with no solution or infinite solutions
Polynomial Equation Solver
The polynomial equation solver mode finds every real root of cubic, quartic, and higher-degree equations — not just quadratics — by scanning the function for sign changes and refining each crossing.
- Cubic and quartic equations
- Reports every real root it finds
- Works on any degree polynomial you type in
Rational Equation Solver
The rational equation calculator mode solves equations built from fractions with x in the denominator, and automatically checks for values that would make a denominator zero.
- Equations with x in the denominator
- Automatic domain/exclusion checking
- Handles equations with multiple fractions
Exponential & Logarithmic Equation Solver
The exponential solver and logarithmic equation solver mode isolates x when it's in an exponent or inside a log, using the same substitution and inverse-operation rules taught in class.
- Equations with x as an exponent
- Equations with x inside ln() or log()
- Numeric refinement for equations without a clean closed form
Inequality Solver
The inequality equation solver mode solves linear inequalities with <, >, ≤, or ≥ and returns the answer in interval notation, flipping the sign automatically when the rules require it.
- Strict and inclusive inequalities
- Automatic sign-flip when needed
- Answer given in interval notation
The Rules Behind The Calculator
Every step this calculator produces comes from one of the standard equation-solving rules below.
| Rule | Idea | Used For |
|---|---|---|
| Inverse Operations | Undo +, −, ×, ÷ in reverse order | One-step and two-step equations |
| Combining Like Terms | Collect x-terms on one side | Variable on both sides |
| Elimination | Add/subtract equations to cancel a variable | Systems of equations |
| Sign-Change Scanning | Root exists where f(x) crosses zero | Polynomial and rational equations |
| Logarithm/Exponent Rules | log(a^x)=x·log(a); a^(log_a x)=x | Exponential and logarithmic equations |
| Inequality Sign-Flip Rule | Flip </> when dividing by a negative | Inequalities |
Why AceCalculator Is Different And Better
Most equation solvers online give you an answer and nothing else. AceCalculator focuses on showing the working, matching classroom notation, and staying fast on any device.
- ✓ Full step-by-step solutions, every mode
- ✓ Six equation types in one tool: linear, system, polynomial, rational, exponential/log, inequality
- ✓ Automatic domain checking on rational equations
- ✓ Clean, classroom-style notation
- ✓ Mobile-friendly and responsive on any device
- ✓ No downloads, no accounts, no signup required
- ✓ Runs entirely in your browser — nothing is stored or sent to a server
More Tools By AceCalculator.com
- Algebra Calculator — full algebra step-by-step solver
- Quadratic Formula Calculator — solve quadratics step by step
- Graphing Calculator — plot and visualize any function
- Matrix Calculator — inverse, determinant, eigenvalues
- Derivative Calculator — basic, implicit & nth-order derivatives
- Integral Calculator — indefinite, definite & double integrals
- Limit Calculator — two-sided, one-sided & infinite limits
- Math Calculators Hub — all maths tools in one place
Frequently Asked Questions
Yes. Every mode — linear, systems of equations, polynomial, rational, exponential/log, and inequalities — is free with no account, signup, or download required.
Yes. Each result comes with a numbered list of steps explaining how the value of x (or the system) was found, plus the final solution written in standard notation.
Yes. Switch to System mode, enter two equations (or toggle to three), and the calculator solves for every variable simultaneously using elimination.
An equation solver finds the exact value(s) that make an equation true and shows the algebra behind that answer. A graphing calculator plots a function's shape across a range of values instead, which is why we keep them as two separate tools — see our Graphing Calculator.
Yes. Polynomial mode finds every real root of cubic, quartic, and higher-degree polynomial equations, not just quadratics, by scanning for sign changes and refining each root with bisection. For classic ax²+bx+c quadratics specifically, our dedicated Quadratic Formula Calculator also shows the discriminant and vertex form.
Yes. Inequality mode solves linear inequalities (using <, >, ≤, or ≥) and returns the answer in interval notation, flipping the inequality sign automatically when required.
This tool scans for real number solutions only, which covers the vast majority of homework and practical problems. If a polynomial has no real roots in the scanned range, the calculator will say so rather than guess.
Linear and system solutions are exact. Polynomial, rational, and exponential/log solutions are refined numerically to six decimal places, which is more than enough precision for coursework — but always double-check results for high-stakes exams or professional work.
Important Disclaimer
AceCalculator's equation solver is provided for informational and educational purposes only. While every step follows standard algebra rules, results are not a substitute for verification by a qualified instructor or professional where accuracy is critical. See our full Disclaimer and Terms and Conditions.