While it is not known today with certainty what method del Ferro used, it is thought that he used the fact that x=\sqrt{a+\sqrt{b}}+\sqrt{a-\sqrt{b}} solves the equation x^2=(2\sqrt{a^2-b})x^0+2a to conjecture that x=\sqrt[3]{a+\sqrt{b}}+\sqrt[3]{a-\sqrt{b}} solves x^3=(3\sqrt[3]{a^2-b})x+2a. This turns out to be true.
