Cubic equation solver
The Cubic equation solver computes cubic equation solver from the relation real roots of a x^3 + b x^2 + c x + d. It takes 4 inputs (a, b, c, d) and returns the real roots. Because this is a pure mathematical or physical formula rather than a jurisdiction-specific rule, the result never changes over time: the same inputs always produce the same answer, so you can rely on it whether you are checking homework, sizing a design, or sanity-checking another tool. Enter your values in the fields below and the result updates instantly; you can also share a permalink that pre-fills the exact calculation, which is useful for teaching, reports, or collaboration. For example, with a = 1, b = 0, c = 0, d = -8, the real roots works out to 2, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. The method is the standard form documented by NIST DLMF, and the figure above each result carries the date it was last verified. This tool is general information and is not a substitute for professional engineering, medical, financial, or scientific advice; always check critical results against the primary source and your own judgement.
With a = 1, b = 0, c = 0, d = -8, the result is 2.
Applies to: any numeric inputs. Method source: NIST DLMF, checked 2026-06-23.
The formula
real roots of a x^3 + b x^2 + c x + d
Worked example
With a = 1, b = 0, c = 0, d = -8:
- depressed cubic + Cardano/trig
- Real roots = 2
This worked example is one of the automated golden-value tests this calculator must pass before it can publish.
What this assumes
- Inputs are real numbers in the units shown.
- The result is the exact value of real roots of a x^3 + b x^2 + c x + d; general information, not professional advice.
Frequently asked questions
What formula does this use?
real roots of a x^3 + b x^2 + c x + d, the standard form documented by NIST DLMF.
Does the result ever change over time?
No. This is a pure formula with no external rate, so the same inputs always give the same result.
Official sources and verification
- Method: NIST DLMF, checked 2026-06-23.
Reviewed by the CalculatorHub team, edited by James Graham, 2026-06-23. See our methodology. General information, not professional advice.