Given xy=-60984 x^2+y^2-20x-20y-121868=0 Find the values x and y?

xy = -60984
y = -60984 / x
x^2 + y^2 - 20x - 20y - 121,868 = 0
x^2 - 20x + 400 + y^2 - 20y + 400 = 121,868 + 800
(x - 20)^2 + ((-60,984 / x) - 20)^2 = 122,668
(x - 20)^2 + [(-60,984 - 20x) / x]^2 = 122,668

Expanding gives a quartic equation, and, much algebra later 4 solutions

x = 10 - 5 sqrt(3) - sqrt(61159 - 100 sqrt(3))
x = 10 - 5sqrt(3) + sqrt(61159 - 100 sqrt(3))
x = 5(2+sqrt(3)) - sqrt(61159+100 sqrt(3))
x = 5(2+sqrt(3)) + sqrt(61159+100 sqrt(3))

Each of these gives an answer for y ... y = -60984 / x
you can do those

Incomplete question