So what was the problem? :)
Let me guess. This problem will come down to solving what is effectively a 4th degree polynomial. The results will look nasty. Lots of roots. Lots of things that say root of. So the solution you got looked like a mess. (Because it is, and it must be so.) The fact is, there is no simple formula for the solution. Certainly not anything that will be easy to look at.
However, there is a simple solution. You know the range in x and y that you care about. So pick a sequence of values for x (or y.) Just loop over this set of values. So for any value of x, now use vpasolve to solve for the solution to your problem, with x substituted into that expression. Or you can use fzero.
For any x, you get the value of y, to a reasonably high degree of precision. You will actually get a set of probably 4 values for y for any x. Pick the REAL root that falls in the region of interest. This gives you a closely spaced set of solutions to the problem. Easy to do. It gives you what you want. And the nice thing is, all of these points on the curve are essentially exact, to within the ability of the solver to give you high accuracy.
You can use a spline to approximate the curve if you want something smooth. No matter what, you WON'T get a simple function, as I said before. So just use a spline in the end.