A history of Cardano's formula

Summary

List of characters

History of the formula

Chronology

References

Proof of the formula

The quadratic formula \(\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\) to solve the quadratic equation \(ax^2+bx+c=0\) (familiar to school children) was already known by the Babylonians, probably as early as 2000 BC. But no progress was made for millennia to find a formula for the cubic \(ax^3+bx^2+cx+d=0\), until at the beginning of the 16th century a dramatic sequence of developments in Italy resulted in the publication in 1545 of what is now known as Cardano's formula. But the formula was not discovered by Cardano, and the history behind its discovery is so full of drama and suspense that it would be possible to make a motion picture out of it.