I will guess that, contrary to standard mathematical practice, you mean "X" and "x" to be the same variable. Also, I will guess that you are wanting to graph y as a function of x.
Given the equation y<sup>2</sup> - sqrt[2]|x|y + x<sup>2</sup> - 20 = 0, I would suggest applying the Quadratic Formula by treating the equation as a quadratic in y. This will give you "y=" in terms of x.
You will get two functions (from the "plus-minus"); graph each to get "the whole picture".
Eliz.