Algebra Calculator

For solving algebra problems online, a dedicated algebra calculator like those found on MathPapa, Symbolab, or Mathway is the best choice. These tools accept typed expressions and equations, then return step-by-step solutions. Unlike a basic scientific calculator, an online algebra calculator can handle variables, simplify expressions, factor polynomials, and solve systems of equations.

Rewrite your equation in the form ax + b = c (linear) or ax² + bx + c = 0 (quadratic), then enter the coefficients. For example, 3x + 2 = 14 is a = 3, b = 2, c = 14, which gives x = 4. The calculator returns the solution along with a step-by-step breakdown. Some other tools also accept typed expressions, inequalities, and systems of equations; this one focuses on linear and quadratic equations.

Algebra is solved by isolating the unknown variable through a sequence of inverse operations — addition, subtraction, multiplication, and division applied to both sides of the equation equally. For quadratic equations, methods such as factoring, completing the square, or the quadratic formula are used. An online algebra calculator automates these steps and shows each transformation so you can follow the logic.

Yes, the TI-84 graphing calculator includes a built-in Equation Solver that can find numerical solutions for algebraic equations. It supports graphing functions, building t-charts, solving systems of equations, and evaluating expressions — making it widely used in college algebra courses. However, an online algebra calculator offers more convenience with instant access, symbolic step-by-step solutions, and no hardware required.

Yes, this algebra calculator supports quadratic equations of the form ax² + bx + c = 0. Enter the coefficients a, b and c and the calculator applies the quadratic formula, returning both roots along with the discriminant and a step-by-step solution. Both real and complex (imaginary) roots are handled.

Yes, the calculator shows the steps for every linear and quadratic equation, not just the final answer. For linear equations it shows how x is isolated; for quadratics it shows the formula, the discriminant and each root. This makes it useful for checking homework and learning the method.

No. This calculator solves linear equations (ax + b = c) and quadratic equations (ax² + bx + c = 0); it does not simplify or factor expressions. To simplify by hand, combine like terms (3x + 5x = 8x), expand brackets (2(x + 3) = 2x + 6) and reduce common factors. If your simplified result is an equation you want solved, enter its coefficients here.

Every one-step, two-step and multi-step equation reduces to the form ax + b = c, which is what the linear solver takes. One-step: x + 7 = 12 is a = 1, b = 7, c = 12, so x = 5. Two-step: 2x + 3 = 11 gives x = 4. Multi-step: first collect terms, so 5x + 2 = 3x + 10 becomes 2x − 8 = 0 (a = 2, b = −8, c = 0) and x = 4. The letter does not matter: to solve −11b + 33 = 44, enter a = −11, b = 33, c = 44 and you get b = −1.

Move every term to one side so the right side is 0. Subtracting 8x and adding 7 gives x² − 3x − 54 = 0, so a = 1, b = −3, c = −54. The discriminant is (−3)² − 4(1)(−54) = 9 + 216 = 225, its square root is 15, and x = (3 ± 15) / 2, which gives x = 9 and x = −6. Check: 9² + 5(9) − 61 = 65 and 8(9) − 7 = 65.

Enter a, b and c and read the roots from the result; they appear as decimals. For 3m² + 11m + 9 = 0 the discriminant is 121 − 108 = 13, so m = (−11 ± √13) / 6, about −1.2324 and −2.4343. For 4n² − 19n + 18 = 0 the discriminant is 361 − 288 = 73, so n = (19 ± √73) / 8, about 3.4430 and 1.3070. A positive discriminant that is not a perfect square means the roots are irrational and the equation does not factor over whole numbers.

Multiply every term by the denominator to clear the fraction. Multiplying by 7 gives 6z + 105 = 651, so a = 6, b = 105, c = 651 and z = (651 − 105) / 6 = 91. Check: (6/7)(91) + 15 = 78 + 15 = 93.

Split it into two linear equations, one with +9 and one with −9, and solve each. 15 + b = 9 gives b = −6 (a = 1, b = 15, c = 9 in the calculator). 15 + b = −9 gives b = −24 (c = −9). Check: |15 − 6| = 9 and |15 − 24| = 9. If the right side is negative, as in |x| = −3, there is no solution.

This calculator takes numbers, so for letters use the same inverse-operation method by hand. ub = j + r: divide both sides by u, so b = (j + r) / u. h = 5nb − xb: factor out b to get h = b(5n − x), so b = h / (5n − x). 5yb = d²b + m: subtract d²b from both sides to get b(5y − d²) = m, so b = m / (5y − d²). b/y − m = d²: add m, then multiply by y, so b = y(d² + m). Once you substitute numbers for the other letters, you can check the answer here.

b² = 0.64 is a quadratic with no middle term: enter a = 1, b = 0, c = −0.64 to get b = ±0.8. Likewise 18x² − 98 = 0 is a = 18, b = 0, c = −98, giving x = ±7/3 (about ±2.3333). For 15x³ − 55x² + 40x = 0, factor out 5x first: 5x(3x² − 11x + 8) = 0, so x = 0 or 3x² − 11x + 8 = 0. Enter a = 3, b = −11, c = 8: the discriminant is 121 − 96 = 25, so x = (11 ± 5) / 6 = 8/3 or 1. The three solutions are x = 0, 1 and 8/3.