DigitHelm

Algebra calculators

These solvers cover school and early college algebra: linear and absolute value equations, inequalities, two-variable systems, quadratics and cubics, polynomial division, exponent and logarithm rules, radicals, complex numbers, and arithmetic and geometric sequences. Most show the method step by step, so they work as a check on your own working rather than a shortcut around it.

20 tools · Updated October 21, 2026

Showing 20 tools
Absolute Value Equation SolverLinear equations and inequalities|2x − 3| = 7x = −2 or x = 5
Arithmetic Sequence CalculatorSequences and sums3, 7, 11, … (first 10 terms)Sum = 210
Completing the Square CalculatorQuadratics and polynomialsy = x² + 6x + 5y = (x + 3)² − 4
Complex Number CalculatorRadicals and complex numbers(3 + 4i)(1 − 2i)11 − 2i
Cubic Equation SolverQuadratics and polynomialsx³ − 6x² + 11x − 6 = 0x = 1, 2, 3
Exponent Rules CalculatorExponents and logarithms2³ × 2⁴2⁷ = 128
Exponential Growth & Decay CalculatorExponents and logarithms1,000 at 25%/hour continuous, 10 hours12,182.5
Geometric Sequence CalculatorSequences and sums3, 6, 12, … (first 8 terms)Sum = 765
Inequality SolverLinear equations and inequalities−3x + 6 > −9x < 5
Linear Equation SolverLinear equations and inequalities5x − 3 = 2x + 9x = 4
Logarithm CalculatorExponents and logarithmslog₂(8)3
Logarithm Laws CalculatorExponents and logarithmslog₁₀(100 × 1,000)2 + 3 = 5
Polynomial EvaluatorQuadratics and polynomialsx³ − 6x² + 11x − 6 at x = 4P(4) = 6
Polynomial Long Division CalculatorQuadratics and polynomials(2x⁴ − 3x² + x + 5) ÷ (x² − x + 2)2x² + 2x − 5 R −8x + 15
Quadratic Equation SolverQuadratics and polynomialsx² − 3x − 10 = 0x = −2 or 5
Rational Root Theorem CalculatorQuadratics and polynomialsRational roots of 2x³ + x² − 13x + 6x = −3, 1/2, 2
Simplify Radicals CalculatorRadicals and complex numbersSimplify √726√2
Summation CalculatorSequences and sumsΣ n² for n = 1 to 10385
Synthetic Division CalculatorQuadratics and polynomials(x³ − 6x² + 11x − 6) ÷ (x − 2)x² − 4x + 3
Systems of Equations Solver 2×2Linear equations and inequalities2x + 3y = 7, x − y = 1x = 2, y = 1

Which one do I need?

I need to solve a one-variable equation like 3x + 7 = 22Linear Equation SolverI have two equations with x and y and need both valuesSystems of Equations Solver 2×2I have ax² + bx + c = 0 and want the roots, vertex and graphQuadratic Equation SolverI want to rewrite a quadratic in vertex formCompleting the Square CalculatorI need to divide one polynomial by another and get the remainderPolynomial Long Division CalculatorI want to solve an inequality and write the answer in interval notationInequality SolverI need log base 10, natural log or a log in any baseLogarithm CalculatorI want the nth term or the sum of a geometric sequenceGeometric Sequence Calculator

From linear equations to polynomials

Solving an equation means applying the same operation to both sides until the variable is alone. Linear equations always have one solution, no solution or infinitely many, and the Linear Equation Solver shows each balancing step. Inequalities follow the same rules with one exception: multiplying or dividing by a negative number flips the inequality sign.

Quadratics have up to two roots, and the discriminant b² − 4ac tells you in advance whether they are two real numbers, one repeated root or a complex pair. The Quadratic Equation Solver reports the discriminant, roots and vertex together. For higher-degree polynomials, the Rational Root Theorem Calculator lists candidate roots, and Synthetic Division or Polynomial Long Division then factors them out one at a time.

Exponents, logarithms and growth

Logarithms undo exponents: log₂ 8 = 3 because 2³ = 8. The laws of logarithms mirror the laws of exponents, turning multiplication into addition and powers into multiplication, which is what makes them useful for solving equations where the unknown is in the exponent. The Exponent Rules and Logarithm Laws calculators show each rule applied to your own expression.

Exponential models describe quantities that change by a constant percentage per period, such as population growth, compound interest or radioactive decay. Use the Exponential Growth and Decay Calculator to find the final value, rate or time, and the Logarithm Calculator when you need the raw log in any base.

Sequences, series and sigma notation

An arithmetic sequence adds the same difference each time (3, 7, 11, 15), while a geometric sequence multiplies by the same ratio (3, 6, 12, 24). Each has a simple formula for the nth term and for the sum of the first n terms, which the matching calculators apply and explain.

Sigma notation is shorthand for adding a pattern of terms. The Summation Calculator evaluates any finite sum you can write as a formula in the index, which is useful when a sequence is neither arithmetic nor geometric.

Questions people ask

For ax² + bx + c = 0, the discriminant b² − 4ac decides the type of roots. A positive value gives two distinct real roots, zero gives one repeated real root, and a negative value gives two complex conjugate roots. It is worth checking before solving because it shows whether a real answer exists.

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