16x²y²-48x²y+24xy²+100x²+16y²-72xy+150x-48y+100=28

Determine the pair(s) of real numbers $(a,\,b)$ that satisfy the equation $16x^2y^2-48x^2y+24xy^2+100x^2+16y^2-72xy+150x-48y+100=28$.

At first glance,  this seems like we need to use the modular arithmetic method to solve for $(x,\,y)$ but wait a minute! We need to find not the integers but real for $(x,\,y)$, so nope, modular arithmetic is out of the question...