Algebra
Linear Equation Calculator
Solve any linear equation in one variable, such as 3x + 5 = 2(x − 4), step by step with the solution checked.
ax + b = 0 ⇒ x = −b / a
Also called solve for x · linear equation solver
Math · 11 calculators
Algebra Calculators
Solve linear, quadratic and cubic equations, systems of equations, inequalities and simplify polynomials.
Algebra
Quadratic Equation Calculator
Solve ax² + bx + c = 0 with the quadratic formula: real or complex roots, discriminant, vertex and factored form.
x = (−b ± √(b² − 4ac)) / 2a
Also called quadratic formula calculator · quadratic solver
Algebra
Cubic Equation Calculator
Solve cubic equations ax³ + bx² + cx + d = 0 for all three roots (real and complex) with the discriminant.
Δ = 18abcd − 4b³d + b²c² − 4ac³ − 27a²d²
Also called cubic solver · third degree equation
Algebra
Equation Solver
Solve almost any equation in x — polynomial, trigonometric, exponential or logarithmic — and find all real solutions in a range.
Rewrite as f(x) = 0 and locate every x wh…
Also called solve equation · equation calculator
Algebra
System of Equations Calculator
Solve systems of 2, 3 or more linear equations (x, y, z …) typed naturally, e.g. 2x + 3y = 13, x − y = −1.
A·x = b ⇒ x = A⁻¹·b (Gaussian elimination)
Also called simultaneous equations · system of linear equations
Algebra
Polynomial Calculator
Add, subtract or multiply two polynomials, evaluate at a point, and find the degree and all roots of the result.
(aₙxⁿ + …)(bₘxᵐ + …) — multiply every ter…
Also called polynomial operations · multiply polynomials
Algebra
Factoring Calculator
Factor polynomials with integer coefficients, such as x³ − 7x + 6 or 6x² + x − 2, into linear and irreducible factors.
Rational root theorem: rational roots are…
Also called factor polynomial · factorise
Algebra
Simplify Expression Calculator
Expand and simplify polynomial expressions like (x + 2)³ − x(x − 1), collecting like terms into standard form.
Distribute, expand powers, then combine l…
Also called simplify algebra · expand brackets
Algebra
Slope Calculator
Find the slope (gradient) of a line through two points, its angle of inclination, and the line equation y = mx + b.
m = (y₂ − y₁) / (x₂ − x₁)
Also called slope formula · gradient calculator
Algebra
Intercept Calculator
Find the x- and y-intercepts of a line from its equation (y = mx + b or Ax + By = C) or from two points.
x-intercept: y = 0
Also called x intercept · y intercept
Algebra
Inequality Calculator
Solve linear and quadratic inequalities in x (<, ≤, >, ≥) and get the answer in interval notation.
Find where the expression equals 0, then …
Also called solve inequality · inequality solver
Key algebra formulas
| Linear Equation | ax + b = 0 ⇒ x = −b / a |
|---|---|
| Quadratic Equation | x = (−b ± √(b² − 4ac)) / 2a |
| Cubic Equation | Δ = 18abcd − 4b³d + b²c² − 4ac³ − 27a²d² |
| Equation Solver | Rewrite as f(x) = 0 and locate every x where f changes sign |
| System of Equations | A·x = b ⇒ x = A⁻¹·b (Gaussian elimination) |
| Polynomial | (aₙxⁿ + …)(bₘxᵐ + …) — multiply every term by every term, then collect like terms |
| Factoring | Rational root theorem: rational roots are ±(factor of constant)/(factor of leading coefficient) |
| Simplify Expression | Distribute, expand powers, then combine like terms |
| Slope | m = (y₂ − y₁) / (x₂ − x₁) |
| Intercept | x-intercept: y = 0 · y-intercept: x = 0 |
Algebra questions
How do I type the equation?
Use x as the variable, * or implied multiplication (2x, 3(x+1)), / for division and ^ for powers. Example: 0.5x - 3 = (x + 7)/4.
What does the discriminant tell you?
If b² − 4ac > 0 there are two real roots, if it equals 0 there is one repeated root, and if it is negative the roots are complex conjugates.
What if the calculator says the matrix is singular?
The equations are dependent or inconsistent — there is either no solution or infinitely many. Check that each equation adds new information.
What does the slope mean?
It is the change in y for each 1-unit increase in x — "rise over run". Positive slopes go up to the right, negative slopes go down, 0 is horizontal and vertical lines have undefined slope.