$\text{a)}$  

$2x^2-3=6-x^2\mid -6+x^2$  

$3x^2-9=0\mid :3$  

$x^2-3=0$  

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

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

$x=\sqrt{3}\text{lub}x=-\sqrt{3}$  

$\text{b)}$      

${\left(\frac{1}{3}x+1\right)}^2=4$  

$\frac{1}{9}{x}^2+\frac{2}{3}x+1=4$  

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

$x^2+6x-27=0$  

$\Delta =6^2-4\cdot 1\cdot \left(-27\right)=36+108=144$  

$x_1=\frac{-6-12}{2}=\frac{-18}{2}=-9$  

$x_2=\frac{-6+12}{2}=\frac{6}{2}=3$  

$\text{c)}$  

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

$9x^2-12x+4=x^2+2x+1\mid -x^2-2x-1$  

$8x^2-14x+3=0$  

$\Delta ={\left(-14\right)}^2-4\cdot 8\cdot 3=196-96=100$  

$x_1=\frac{14-10}{2\cdot 8}=\frac{4}{16}=\frac{1}{4}$  

$x_2=\frac{14+10}{2\cdot 8}=\frac{24}{16}=\frac{6}{4}=\frac{3}{2}$  

$\text{d)}$  

$\left(2x-4\right)\left(2x+3\right)=1-11x$  

$4x^2+6x-8x-12=1-11x\mid -1+11x$  

$4x^2+9x-13=0$  

$\Delta =9^2-4\cdot 4\cdot \left(-13\right)=81+208=289$  

$x_1=\frac{-9-17}{2\cdot 4}=\frac{-26}{8}=-\frac{13}{4}$  

$x_2=\frac{-9+17}{2\cdot 4}=\frac{8}{8}=1$