Clearly by inspection x=y=7 is one solution.
There are seven other solutions where x and y are different (fourteen if you swap x and y).
Fifteen solutions total.
(-8,-5),(-8,-3),(-5,-8),(-5,3),(-3,-8),(-3,5),(0,7),(3,-5),(3,8),(5,-3),(5,8),(7,0),(7,7),(8,3),(8,5)
If the equation is rearranged to avoid dividing by zero, there are three other solutions involving x and/or y being -7:
(-7,-7),(-7,0),(0,-7) but these do not solve the equation as presented.
brute force
