$a)-7x^2+42x=0\mid :\left(-7\right)$

$x^2-6x=0$

$x\left(x-6\right)=0$

$x=0lubx-6=0$

$x=6$

$x\in \left\{0,6\right\}$

 

$b)9x^2+\frac{1}{3}x=0\mid \cdot 3$

$27x^2+x=0$

$x\left(27x+1\right)=0$

$x=0lub27x+1=0\mid -1$

$27x=-1\mid :27$

$x=-\frac{1}{27}$

$x\in \left\{-\frac{1}{27},0\right\}$

 

 

 

$c)36x^2=6x\mid -6x$

$36x^2-6x=0\mid :6$

$6x^2-x=0$

$x\left(6x-1\right)=0$

$x=0lub6x-1=0$

$6x=1\mid :6$  

$x=\frac{1}{6}$        

 

 

 

$d)2x+18x^2=0\mid :2$

$x+9x^2=0$

$x\left(1+9x\right)=0$

$x=0lub1+9x=0\mid -1$

$9x=-1\mid :9$

$x=-\frac{1}{9}$

$x\in \left\{-\frac{1}{9},0\right\}$

 

 

 

 

$e)\sqrt{2}{x}^2-\sqrt{8}x=0$

$\sqrt{2}{x}^2-\sqrt{4}\cdot \sqrt{2}x=0$

$\sqrt{2}{x}^2-2\sqrt{2}x=0\mid :\sqrt{2}$

$x^2-2x=0$

$x\left(x-2\right)=0$

$x=0lubx-2=0$

$x=2$

 

 

 

 

$f)\sqrt{3}x=-3x^2\mid =3x^2$

$3x^2+\sqrt{3}x=0$

$x\left(3x+\sqrt{3}\right)=0$

$x=0lub3x+\sqrt{3}=0\mid -\sqrt{3}$

$3x=-\sqrt{3}\mid :3$

$x=-\frac{\sqrt{3}}{3}$

$x\in \left\{-\frac{\sqrt{3}}{3},0\right\}$