$\text{a)}{x}^2-7x=0$  

$x\left(x-7\right)=0$  

$x=0\text{lub}x-7=0$  

$x=0\text{lub}x=7$  

$\text{b)}6x^2+15x=0\mid :6$  

$x^2+\frac{5}{2}x=0$  

$x\left(x+\frac{5}{2}\right)=0$  

$x=0\text{lub}x+\frac{5}{2}=0$  

$x=0\text{lub}x=-\frac{5}{2}$  

$\text{c)}9x-8x^2=0$  

$8x^2-9x=0\mid :8$  

$x^2-\frac{9}{8}x=0$  

$x\left(x-\frac{9}{8}\right)=0$  

$x=0\text{lub}x-\frac{9}{8}=0$  

$x=0\text{lub}x=\frac{9}{8}$  

$\text{d)}x-\frac{1}{4}{x}^2=0$  

$\frac{1}{4}{x}^2-x=0\mid \cdot 4$  

$x^2-4x=0$  

$x\left(x-4\right)=0$  

$x=0\text{lub}x-4=0$  

$x=0\text{lub}x=4$  

$\text{e)}\sqrt{6}x-3x^2=0$  

$3x^2-\sqrt{6}x=0\mid :3$  

$x^2-\frac{\sqrt{6}}{3}x=0$  

$x\left(x-\frac{\sqrt{6}}{3}\right)=0$  

$x=0\text{lub}x-\frac{\sqrt{6}}{3}=0$  

$x=0\text{lub}x=\frac{\sqrt{6}}{3}$  

$\text{f)}\sqrt{6}{x}^2-3x=0\mid :\sqrt{6}$  

$x^2-\frac{3}{\sqrt{6}}x=0$  

$x\left(x-\frac{3}{\sqrt{6}}\right)=0$  

$x=0\text{lub}x-\frac{3}{\sqrt{6}}=0$  

$x=0\text{lub}x=\frac{3}{\sqrt{6}}=\frac{3}{\sqrt{6}}\cdot \frac{\sqrt{6}}{\sqrt{6}}=\frac{3\sqrt{6}}{6}=\frac{\sqrt{6}}{2}$  

$x=0\text{lub}x=\frac{\sqrt{6}}{2}$