Advanced Math Solver
Algebra · Calculus · Statistics · Trigonometry · Matrix — step-by-step solutions
2x² + 5x - 3 = 0 (degree 2)Δ = b² - 4ac = 5² - 4(2)(-3) = 49x = (-b ± √Δ) / 2ax₁ = (-5 + 7) / 4 = 1/2 and x₂ = (-5 - 7) / 4 = -3
Math Solver: Free Step-by-Step Algebra, Calculus & Statistics Solver
A math solver turns a typed problem into a worked answer. This free online math solver handles algebra, calculus, statistics, trigonometry and matrices from a single input box, and it works out for itself what kind of problem you entered. Every result comes with numbered steps and, where it helps, a graph, so you can solve a quadratic, find a derivative, integrate a function, analyze a data set or invert a matrix without switching tools or creating an account.
Quick answer: to solve 2x² + 5x − 3 = 0, the discriminant is 5² − 4(2)(−3) = 49, so x = (−5 ± 7) / 4, which gives x = 1/2 and x = −3. For a calculus example, the derivative of 3x² + 2x is 6x + 2. Type your own problem above and press Solve to see the same kind of working.
What This Math Solver Can Do
For algebra it solves linear, quadratic, cubic and higher-degree equations, equations with fractions, trig or exponential terms, systems of up to five linear equations and inequalities, and it expands, factors and simplifies expressions. In calculus it finds derivatives of any order, indefinite and definite integrals, improper integrals, limits, sums and simple differential equations. It also returns full statistics for a list of numbers, all six trig values with exact answers for special angles, and matrix results for determinants, inverses, rank, products and powers up to 6×6.
Formulas and Methods Used
Each answer uses a standard method, and the steps name it. Quadratics use the quadratic formula, while higher degrees are tested for rational roots first and then solved numerically.
Derivatives use the sum, product, quotient and chain rules. Integrals use substitution, integration by parts and partial fractions when the power rule is not enough, and each answer is verified by differentiating it. Systems and matrices use Gauss-Jordan elimination. Here are a few examples of what you can type:
| You type | Type of problem | Result |
|---|---|---|
| 2x^2 + 5x - 3 = 0 | Equation | x₁ = -3, x₂ = 1/2 |
| 2x + y = 5; x - y = 1 | Linear system | x = 2, y = 1 |
| x^2 - 4 > 0 | Inequality | (-∞, -2) ∪ (2, ∞) |
| d/dx(3x^2 + 2x) | Derivative | 6x + 2 |
| ∫(x^2 + 2x) dx | Integral | x³/3 + x² + C |
| ∫_0^3 (x^2) dx | Definite integral | 9 |
| lim(x→0)(sin(x)/x) | Limit | 1 |
| det([[3,8],[4,6]]) | Matrix | -14 |
| 4, 8, 6, 5, 3, 2, 8, 9, 2, 5 | Statistics | mean 5.2, median 5 |
How to Type Math Correctly
Write problems the way they appear in a textbook, using a few simple conventions. The Math Input button opens a keyboard with templates for fractions, roots, integrals, limits and matrices, and pressing Enter solves the problem.
| To write | Type this | Example |
|---|---|---|
| Power or exponent | ^ or the ² key | x^3 - 2x^2 |
| Square or cube root | sqrt() or cbrt() | sqrt(x + 4) |
| Fraction | / with brackets | (x + 1)/(x - 1) |
| Pi, e and infinity | pi, e, inf | 2pi, e^(2x) |
| Trig in degrees | ° after the number | sin(30°) |
| Logarithms | ln() or log() | ln(x) + log(x) |
| Factorial, combinations | ! and nCr(n,k) | nCr(10,3) |
| Sum and product | sum(k,start,end,expr) | sum(k,1,10,k^2) |
Statistics, Trigonometry and Matrices
Paste a list of numbers and the solver returns the mean, median, mode, sample and population standard deviation, quartiles and outliers. For a quick average, the mean median mode calculator is faster, and the standard deviation calculator focuses on spread alone. Trig inputs accept degrees and radians, such as sin(30°) or cos(pi/3), and can work backwards from a value with asin(0.5). For everyday arithmetic, use the scientific calculator, percentage calculator or fraction calculator.
Limits of an Online Math Solver
A solver is a study aid, not a replacement for understanding the method. It does not read photos or word problems, integrals are exact only for the forms it recognizes, limits are numerical estimates, and equations that are not polynomials are solved numerically between −50 and 50. If a result looks surprising, substitute the answer back in or compare it with your own working.
Who Uses This Math Solver?
High school and college students use it to check homework in algebra, calculus and statistics. Teachers and tutors use it to prepare worked examples, and engineers, analysts and researchers use it for quick checks on derivatives, integrals, matrices and data summaries.
How to Use This Math Solver
Type your problem
Enter an equation, expression, derivative, integral, limit, matrix or list of numbers. Tap an example chip to fill it instantly.
Use Math Input if you need symbols
Press Math Input to open the keyboard for fractions, roots, powers, integrals, limits, matrices and Greek letters.
Press Solve
The solver detects the type of problem and shows the answer with numbered steps. Press Enter for the same result.
Review the steps and graph
Follow the method, check the graph, and use Copy to save the answer.