How to solve nonlinear equations?

I am trying to find the y variable in this problem: H = 0.5*(x^2+y^2)+y*x^2-(y^3)/3. H values change between 1/20:1/2, and x values change -2:2. I tried to calculate every y value in these conditions but I couldn’t. How can I solve it?

That’s just a (cubic) polynomial in y, so you could use any package for polynomial roots, e.g. PolynomialRoots.jl or Polynomials.jl.

There’s always the old-fashioned way


Thank you, these were useful for me. I understood my problem better.