$\text{a)}$  

$3{\left(x-2\right)}^2=9\left(x-2\right)$  

$3{\left(x-2\right)}^2-9\left(x-2\right)=0$  

$3\left(x-2\right)\cdot \left[\left(x-2\right)-3\right]=0\mid :3$

$\left(x-2\right)\left(x-5\right)=0$    

$x-2=0\vee x-5=0$  

$x=2\vee x=5$  

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$\text{b)}$  

${\left(x+3\right)}^2=4{\left(x-1\right)}^2$  

$x^2+6x+9=4\left(x^2-2x+1\right)$  

$x^2+6x+9=4x^2-8x+4$  

$0=3x^2-14x-5$  

$\Delta ={\left(-14\right)}^2-4\cdot 3\cdot \left(-5\right)=196+60=256$  

$x_1=\frac{14-16}{2\cdot 3}=\frac{-2}{6}=-\frac{1}{3}$  

$x_2=\frac{14+16}{2\cdot 3}=\frac{30}{6}=5$

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$\text{c)}$  

${\left(2x^2-1\right)}^2={\left(x^2-5\right)}^2$  

Podstawmy  $x^2=t$  

${\left(2t-1\right)}^2={\left(t-5\right)}^2$  

$4t^2-4t+1=t^2-10t+25$  

$3t^2+6t-24=0\mid :3$  

$t^2+2t-8=0$  

$\Delta =2^2-4\cdot 1\cdot \left(-8\right)=4+32=36$  

$t_1=\frac{-2-6}{2}=\frac{-8}{2}=-4$  

$t_2=\frac{-2+6}{2}=\frac{4}{2}=2$  

Zatem otrzymujemy:

$x^2=-4\vee x^2=2$  

$\text{sprzecznosˊcˊ}\vee x=\sqrt{2}\vee x=-\sqrt{2}$