A new approach to solving the cubic: Cardan’s solution revealed

Source abstract

The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics. This article describes five fundamental parameters of the cubic (δ, λ, h , x N , and y N ), and shows how they lead to a significant modification of the standard method of solving a cubic, generally known as Cardan’s solution.