Given the function $\displaystyle 5x^2+8xy+5y^2 = 45$ find the derivative and horizontal tangent(s).

I've obtained the derivative as

$\displaystyle dy/dx = (-5x-4y)/(4x+5y)$

However i am confused about the horizontal tangent, i understand that a tangent is horizontal when $\displaystyle dy/dx = 0$, but i am unsure of what to do next.

$\displaystyle 0 = (-5x-4y)/(4x+5y)$

I'm not after the answer, but the next step(s) required.