Babylonians solve quadratics in radicals.

Euclid demonstrates a geometrical construction for solving a quadratic.

Arab mathematicians reduce:

to a quadratic.

Omar Khayyam (1050-1123) solves cubics geometrically by intersecting parabolas and circles.

Al-Kashi solves special cubic equations by iteration.

Nicholas Chuqet (1445?-1500?) invents a method for solving polynomials iteratively.

Scipione del Ferro (1465-1526) solves the cubic:

but does not publish his solution.

Niccolo Fontana (Tartaglia) (1500?-1557) wins a mathematical contest by solving many different cubics, and gives his method to Cardan.

Girolamo Cardan (1501-1576) gives the complete solution of cubics in his book, The Great Art, or the Rules of Algebra. Complex numbers had been rejected for quadratics as absurd, but now they are needed in Cardan's formula to express real solutions. The Great Art also includes the solution of the quartic equation by Ludovico Ferrari (1522-1565), but it is played down because it was believed to be absurd to take a quantity to the fourth power, given that there are only three dimensions.