$\text{a)}4x^2-5x=0\mid :4$  

$x^2-\frac{5}{4}x=0$  

$x\left(x-\frac{5}{4}\right)=0$  

$x=0\text{lub}x-\frac{5}{4}=0$  

$x=0\text{lub}x=\frac{5}{4}$  

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$\text{b)}x=\sqrt{2}{x}^2$  

$\sqrt{2}{x}^2-x=0\mid :\sqrt{2}$  

$x^2-\frac{1}{\sqrt{2}}x=0$  

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

$x=0\text{lub}x-\frac{1}{\sqrt{2}}=0$  

$x=0\text{lub}x=\frac{1}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$  

$x=0\text{lub}x=\frac{\sqrt{2}}{2}$  

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$\text{c)}25x^2-1=0\mid :25$  

$x^2-\frac{1}{25}=0$  

$x^2=\frac{1}{25}$  

$x=-\frac{1}{5}\text{lub}x=\frac{1}{5}$  

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$\text{d)}1-\frac{81}{16}{x}^2=0$  

$\frac{81}{16}{x}^2=1\mid \cdot \frac{16}{81}$  

$x^2=\frac{16}{81}$  

$x=-\frac{4}{9}\text{lub}x=\frac{4}{9}$  

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$\text{e)}x\left(x+2\right)=-1$  

$x^2+2x+1=0$  

${\left(x+1\right)}^2=0$  

$x+1=0$  

$x=-1$  

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$\text{f)}x\left(x-8\right)=4\left(x-9\right)$  

$x^2-8x=4x-36$  

$x^2-12x+36=0$  

${\left(x-6\right)}^2=0$  

$x-6=0$  

$x=6$