Ok, I'll try to frame my question more clearly this time.
Goal: Find a solution of x^3 + 6x  20 = 0 and express it in the simplest possible form.
Condition: Not allowed to use trialanderror guessing of rational roots or foreknowledge of the solution.
Hint: Applying Cardano's method gives:
x = cube root(10+sqrt(108)) + cube root(10sqrt(108)), but this may or may not be the simplest possible way of expressing this solution.
