Free Advanced Equations Calculators

Quartic Equation Solver | ax⁴+bx³+cx²+dx+e=0

Solve quartic equations (ax⁴+bx³+cx²+dx+e=0) and find all four roots — real and complex — with step-by-step working, factored form, and root verification.

3-Variable System of Equations Solver | 3×3

Solve systems of three linear equations with three unknowns using Gaussian elimination. Handles unique, no solution, and infinite solution cases with full step-by-step row operations.

Partial Fraction Decomposition Calculator

Decompose rational expressions P(x)/Q(x) into partial fractions. Handles linear, repeated linear, and irreducible quadratic denominator factors with step-by-step coefficient solving.

Piecewise Function Calculator & Evaluator

Define piecewise functions with up to 4 pieces, evaluate at any x, check continuity at breakpoints, identify discontinuity types, and view a table of values. Supports standard math expressions.

Exponential & Logarithmic Equation Solver

Solve all standard exponential and logarithmic equations — a·bˣ=c, eˣ=c, log₂(x)=c, ln(ax+b)=c, and quadratic-in-exponential forms — with complete step-by-step algebraic working.

Discrete Fourier Transform (DFT) Calculator | Spectrum Analysis

Compute the Discrete Fourier Transform of any signal sequence of up to 16 samples. Displays each frequency bin's magnitude, phase (radians and degrees), and real and imaginary components in a full results table. Computes the Inverse DFT to verify signal reconstruction and includes common signal presets.

Simplex Method Calculator | Linear Programming Step-by-Step

Solve two-variable linear programming problems with the simplex method. Enter the objective function (maximize or minimize) and up to four inequality constraints. Displays the initial tableau, each pivot operation with entering and leaving variables, and the final optimal solution with all basic feasible solutions listed.

Queuing Theory Calculator | M/M/1 & M/M/c Queue Metrics

Model M/M/1 (single-server) and M/M/c (multi-server) Poisson arrival queues. Computes server utilization ρ, average number in system L, average queue length Lq, mean system time W, mean wait time Wq, and probability P(n) of exactly n customers.