$\begin{align}
& \frac{3}{2}\cos x-{{\sin }^{2}}x=\frac{3}{2}\cos x-(1-{{\cos }^{2}}x)=0 \\
& \Rightarrow 2{{\cos }^{2}}x+3\cos x-2=0 \\
& \Rightarrow \cos x=\frac{-3\pm \sqrt{25}}{4}=\frac{-3\pm 5}{4} \\
& \Rightarrow \left\{ \begin{matrix}
\cos x=-2\,\,\,nadorost \\
\cos x=\frac{1}{2} \\
\end{matrix} \right. \\
& \Rightarrow \cos x=\frac{1}{2}=\cos \frac{\pi }{3}\Rightarrow x=2k\pi \pm \frac{\pi }{3} \\
\end{align}$