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Quartic Equation Solver

Solve ax⁴ + bx³ + cx² + dx + e = 0 for all four roots (real and complex) with a Durand–Kerner numeric solver and step-by-step results.

Related tools

All Algebra & equations tools →
Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.Cubic Equation SolverSolve ax³ + bx² + cx + d = 0 for all three roots (real and complex), with the discriminant, the nature of the roots and steps.Exponential Equation SolverSolve exponential equations of six types — basic, coefficient, linear exponent, two bases, quadratic-in-a^x and shifted — with logarithms and a full step-by-step solution.Linear Equation SolverSolve linear equations like 2x + 3 = 7, x/2 + 4 = 7 or 7x − 5 = 3x + 11 in one variable, with exact fractions and step-by-step working.Literal Equation SolverRearrange a formula to solve for any variable — e.g. A = pi*r^2 gives r = sqrt(A/pi) — with genuine symbolic isolation for linear, power and product forms.Logarithmic Equation SolverSolve logarithmic equations of six types — basic, linear, two logs, sum of logs, exponential and change of base — with step-by-step working, base e support, and extraneous-root rejection.Radical Equation SolverSolve square-root equations by isolating and squaring, then checking every candidate in the original equation to drop extraneous roots — four structured forms with step-by-step working.Rational Equation SolverSolve rational (fraction) equations by clearing denominators to a polynomial, then excluding roots that make any denominator zero — reporting solutions, excluded values, no-solution and identity cases.

Quartic Equation Solver is free to use as often as you like, directly from this page. It sits under Algebra & equations in our catalogue, alongside Absolute Value Equation Solver and Cubic Equation Solver.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Quartic Equation Solver?

Solve ax⁴ + bx³ + cx² + dx + e = 0 for all four roots (real and complex) with a Durand–Kerner numeric solver and step-by-step results.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Quartic Equation Solver different from Absolute Value Equation Solver?

They sit next to each other but answer different questions: Absolute Value Equation Solver is the one to open when you need it to solve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Cubic Equation Solver is the closest one after this: Solve ax³ + bx² + cx + d = 0 for all three roots (real and complex), with the discriminant, the nature of the roots and steps.

What else is worth having open alongside it?

Exponential Equation Solver and Linear Equation Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.