The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3 + a_2 z^2 + a_1 z + a_0 = 0 (the coefficient a_3 of z^3 may be taken as 1 without loss of generality by dividing the entire equation through by a_3). The Wolfram Language can solve cubic equations exactly using the built-in command Solve[a3 x^3 + a2 x^2 + a1 x + a0 == 0, x]. The solution can also be expressed in terms of the Wolfram Language algebraic root objects by first issuing SetOptions[Roots, Cubics -> False].

casus irreducibilis | cubic equation | cubic polynomial | polynomial discriminant | quadratic equation | quartic equation | quintic equation | sextic equation