I am trying to find an analytic solution to a cubic equation of the form ax^3 + cx + d, where a, c, and d are rather complicated coefficients. If I simply use the solve command, it gives the solutions assuming that the discriminant is negative (that is, one real and two imaginary solutions). However, I want the solutions in the case that the discriminant is positive (the solutions have a different functional form; it's not the case that the imaginary solutions simply become real). I've tried using assume (equation for discriminant >0) after the solve command; however, Maple simply eats up all of my available memory instead of giving me the solutions.
So, my question is, how do I get the correct analytic solutions to a cubic equation assuming that the discriminant is positive instead of negative?
Thank you for your time and help.