Algorithm which adapt (solve) the complex equations ( implicit function f(x,y) )

Question

I\'m trying to adapt some equations (implicit f(x,y)) in order to be able list the Y for corresponding X-Value.
The equations could be e.g. as follows:

y^2 =         


        

Answer 1

There ia a possible solution for the general quintic equation, when you addapt the solutionmethod from Cardano for the general cubic equation and the solutionmethod from Ferrari for the general quartic equation.