for the equation 4 cos alpha - square root 12 = 0

Is there more?

What are we doing?
solving?

4cosØ= √12 = 2√3
cosØ = √3/2

I happen to know that cos 30° = √3/2
so Ø = 30° or 330°
in radians: Ø (or your alpha, makes no difference) = π/6 or 11π/6