${{\operatorname{Sin}}^{2}}x=1-{{\operatorname{Cos}}^{2}}x,2{{\operatorname{Sin}}^{2}}x+3\operatorname{Cos}x=0\Rightarrow 2(1-{{\operatorname{Cos}}^{2}}x)+3\operatorname{Cos}x=0$ $\Rightarrow -2{{\operatorname{Cos}}^{2}}x+3\operatorname{Cos}x+2=0\xrightarrow{\times (-1)}2{{\operatorname{Cos}}^{2}}x-3\operatorname{Cos}x-2=0$  $\Delta ={{b}^{2}}-4ac=9-4(2)(-2)=25$ $\Rightarrow \operatorname{Cos}x=\frac{-b\pm \sqrt{\Delta }}{2a}=\frac{3\pm 5}{4}\Rightarrow \left\{ _{\operatorname{Cos}x=-\frac{1}{2}=\operatorname{Cos}\frac{2\pi }{3}\Rightarrow x=2k\pi \pm \frac{2\pi }{3}}^{\operatorname{Cos}x=2} \right.$