# 2sin^(2)x+3cos x=0 solve the equation

$2{\mathrm{sin}}^{2}x+3\mathrm{cos}x=0$ solve the equation
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$2{\mathrm{sin}}^{2}x+3\mathrm{cos}x=0$
$2\left(1-{\mathrm{cos}}^{2}x\right)+3\mathrm{cos}x=0$
$2-2{\mathrm{cos}}^{2}x+3\mathrm{cos}x=0$
$2{\mathrm{cos}}^{2}x-3\mathrm{cos}x-2=0$
$\mathrm{cos}x=a,|a|\le 1$
$2{a}^{2}-3a-2=0$
$D=9+16=25$
$a=\frac{3±5}{4}$
${a}_{1}=2$ does not satisfy
${a}_{2}=-\frac{1}{2}$
$\mathrm{cot}x=-\frac{1}{2}$
$x=±\frac{2\pi }{3}+2\pi k,k\in Z$

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