For curve $\displaystyle x^3 + y^3 - 9xy = 0 $ find x co-ordinates where the tangent to the curve is horizontal.

I differentiated: $\displaystyle \frac{d}{dx}[x^3 + y^3 - 9xy] = \frac{3y - x^2}{y^2 - 3x} $

Let this equal zero for horizontal tangents, but I don't know how to solve from here, the answer is $\displaystyle 54^{\frac{1}{3}} $ but my answers always seem to have a y term in them.

Thanks in advance,