Let y = x^1/4.  

Then the original equation becomes y^2 + y - 20 = 0

It's a simple quadratic with solutions y = -5 or +4.

Therefore, x = y^4 = 625 or 64.

Since we're raising y to the 2nd or 4th power to find x, i.e., not taking roots with the attendant sign issues, there doesn't seem to be anything more.