The opening historical box told of the Tartaglia–Cardano rivalry. Here we see concretely the Cardano formula for solving third-degree equations: it is the natural generalisation of the Δ\Delta formula for the second degree, and it is the real reason why the mathematicians of the Renaissance had to surrender to the existence of imaginary numbers. The path passes through two moves: reducing the equation to the depressed form and then applying the solving formula.