A cubic equation is an equation involving a cubic
polynomial, i.e., one of the form
Since
(or else the polynomial would be quadratic and not cubic), this can without loss
of generality be divided through by , giving
A closed-form formula known as the cubic formula
exists for the solutions of a cubic equation.
Omar Khayyam's Al-jabr, written around 1070-1079, gave the first systematic treatment of classes of cubic equations and geometrically solved the six forms having
one term equal to a sum of two others. A thirteenth-century manuscript of the work
is shown above (Berggren 2007, Merzbach and Boyer 2011).
Cardano (1545) gave the first published algebraic solution of the general cubic in Ars magna. The page illustrated above opens Chapter XI, which treats the case
and gives a geometric demonstration
of its solution.
(or else the polynomial would be quadratic and not cubic), this can without loss
of generality be divided through by 
, giving
,
Khayyam constructed the intersection of a parabola
with a semicircle; the relevant abscissa
gives the positive solution.
and gives a geometric demonstration
of its solution.
