Paraphrasing Wikipedia > Cubic Equation > General cubic formula, and ignoring special cases and caveats, it says:
The cubic equation:
$$ax^3 + bx^2 + cx + d = 0$$
can be solved as follows:
Let:
$$\Delta_0 = b^2 - 3ac$$ $$\Delta_1 = 2b^3 - 9abc + 27a^2d$$
$$C = \sqrt[3]{{\Delta_1 \pm \sqrt{\Delta_1^2 - 4 \Delta_0^3}}\over{2}}$$
One of the roots is:
$$x = - {{1} \over {3a}}(b + C + {\Delta_0 \over C}) $$
The other two roots can be obtained by changing the choice of the cube root in the definition of C.
What does it mean "changing the choice of the cube root in the definition" of C?