$\text{a)}{x}^3+3x^2+2x=0$  

$x\left(x^2+3x+2\right)=0$  

$x=0\text{lub}{x}^2+3x+2=0$  

$\Delta =3^2-4\cdot 1\cdot 2=9-8=1,\sqrt{\Delta }=\sqrt{1}=1$  

$x=\frac{-3-1}{2}=\frac{-4}{2}=-2\text{lub}x=\frac{-3+1}{2}=\frac{-2}{2}=-1$  

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$\text{b)}{x}^3+2x^2-15x=0$  

$x\left(x^2+2x-15\right)=0$  

$x=0\text{lub}{x}^2+2x-15=0$  

$\Delta =2^2-4\cdot 1\cdot \left(-15\right)=4+60=64,\sqrt{\Delta }=\sqrt{64}=8$  

$x=\frac{-2-8}{2}=\frac{-10}{2}=-5\text{lub}x=\frac{-2+8}{2}=\frac{6}{2}=3$  

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$\text{c)}2x^4-5x^3-3x^2=0$  

$x^2\left(2x^2-5x-3\right)=0$  

$x^2=0\text{lub}2x^2-5x-3=0$  

$x=0\Delta ={\left(-5\right)}^2-4\cdot 2\cdot \left(-3\right)=25+24=49,\sqrt{\Delta }=\sqrt{49}=7$  

$x=\frac{5-7}{2\cdot 2}=\frac{-2}{4}=-\frac{1}{2}\text{lub}x=\frac{5+7}{2\cdot 2}=\frac{12}{4}=3$  

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$\text{d)}2x^4-12x^3+18x^2=0$  

$2x^2\left(x^2-6x+9\right)=0$  

$2x^2=0\text{lub}{x}^2-6x+9=0$  

$x=0{\left(x-3\right)}^2=0$  

$x-3=0$  

$x=3$