I am to find the number of points (by hand ) where the curve x^2 - xy + (3/4)y^2 = 7 has horizontal tangent lines.

what i did was i took the derivative:

2x-y+(3/2)y = 0

simplified:

2x - (1/2) y = 0

solved for y:

2x = (1/2)y

4x = y

plugged it into the original to find my x value

x=+/- sqrt(7)/3

what do i do from here?