$\text{a)}{x}^3-1=0$  

$\left(x-1\right)\left(x^2+x+1\right)=0$  

$x-1=0\vee \underset{\text{roˊwnanie sprzeczne,}\Delta <0}{\underbrace{x^2+x+1=0}}$  

$x=1$  

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$\text{b)}2x^5-x=0$  

$x\left(2x^4-1\right)=0$  

$x\left(\sqrt{2}{x}^2-1\right)\left(\sqrt{2}{x}^2+1\right)=0$  

$x\left(\sqrt[4]{2}x-1\right)\left(\sqrt[4]{2}x+1\right)\left(\sqrt{2}{x}^2+1\right)=0$  

$x=0\vee \sqrt[4]{2}x-1=0\vee \sqrt[4]{2}x+1=0\vee {\sqrt{x}}^2+1=0$  

$x=0\vee \sqrt[4]{2}x=1\left|:\sqrt[4]{2}\vee \sqrt[4]{2}x=-1\right|:\sqrt[4]{2}\vee \underset{\text{roˊwnanie sprzeczne}}{\underbrace{{\sqrt{x}}^2=-1}}$  

$x=0\vee x=\frac{1}{\sqrt[4]{2}}\vee x=-\frac{1}{\sqrt[4]{2}}$  

$x\in \left\{-\frac{1}{\sqrt[4]{2}},0,\frac{1}{\sqrt[4]{2}}\right\}$  

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$\text{c)}{\left(x^2-9\right)}^2-4=0$  

$\left(x^2-9-2\right)\left(x^2-9+2\right)=0$  

$\left(x^2-11\right)\left(x^2-7\right)$  

$\left(x-\sqrt{11}\right)\left(x+\sqrt{11}\right)\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)=0$  

$x-\sqrt{11}=0\vee x+\sqrt{11}=0\vee x-\sqrt{7}=0\vee x+\sqrt{7}=0$  

$x=\sqrt{11}\vee x=-\sqrt{11}\vee x=\sqrt{7}\vee x=-\sqrt{7}$  

$x\in \left\{-\sqrt{11},-\sqrt{7},\sqrt{7},\sqrt{11}\right\}$  

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$\text{d)}-2x^3-2x+4=0\mid :\left(-2\right)$

  $x^3+x-2=0$  

$x^3-x^2+\underset{\Delta =9}{\underbrace{x^2+x-2}}=0$  

$x^2\left(x-1\right)+\left(x+2\right)\left(x-1\right)=0$  

$\left(x-1\right)\left(x^2+x+2\right)=0$  

$x-1=0\vee \underset{\text{roˊwnanie sprzeczne,}\Delta <0}{\underbrace{x^2+x+2=0}}$  

$x=1$