What you did was mathematically correct but it doesn't help
isolate y.
x² + xy + y² = 9
First get 0 on the right
x² + xy + y² - 9 = 0
Rearrange in descending powers of y:
y² + xy + x² - 9 = 0
Think of it as a quadratic equation in y this way:
1y^2 + xy + (x²-9) = 0
Then use the quadratic formula
where a = 1, b = x, c = (x²-9)
Edwin