$\text{a)}$  

$\frac{\left(2x+3\right)\left(1-x\right)}{6}-\frac{x+2}{4}=x^2-\frac{\left(x-1\right)x}{3}\mid \cdot 12$  

$2\left(2x+3\right)\left(1-x\right)-3\left(x+2\right)=12x^2-4\left(x-1\right)x$  

$2\left(2x-2x^2+3-3x\right)-3x-6=12x^2-4x^2+4x$  

$2\left(-2x^2-x+3\right)-3x-6=8x^2+4x$  

$-4x^2-2x+6-3x-6=8x^2+4x$  

$-4x^2-5x=8x^2+4x$  

$-12x^2-9x=0$  

$x\left(-12x-9\right)=0$  

$x=0\vee -12x-9=0$  

$x=0\vee -12x=9$  

$x=0\vee x=-\frac{9}{12}$  

$x=0\vee x=-\frac{3}{4}$  

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$\text{b)}$  

$\frac{\left(x+2\right)\left(2-x\right)}{4}-\frac{2x^2-0,5}{2}=\frac{{\left(2-5x\right)}^2-{\left(4x-1\right)}^2}{8}\mid \cdot 8$  

$2\left(x+2\right)\left(2-x\right)-4\left(2x^2-0,5\right)={\left(2-5x\right)}^2-{\left(4x-1\right)}^2$  

$2\left(2x-x^2+4-2x\right)-8x^2+2=4-20x+25x^2-\left(16x^2-8x+1\right)$  

$2\left(-x^2+4\right)-8x^2+2=4-20x+25x^2-16x^2+8x-1$  

$-2x^2+8-8x^2+2=9x^2-12x+3$  

$-10x^2+10=9x^2-12x+3$  

$-19x^2+12x+7=0$  

$\Delta ={12}^2-4\cdot \left(-19\right)\cdot 7=144+532=676$  

$\sqrt{\Delta }=26$  

$x_1=\frac{-12-26}{2\cdot \left(-19\right)}=\frac{-38}{-38}=1$  

$x_2=\frac{-12+26}{2\cdot \left(-19\right)}=\frac{14}{-38}=-\frac{7}{19}$  

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$\text{c)}$  

$\frac{{\left(4x-3\right)}^2-8+60x}{15}=\frac{\left(-2x-3\right)\left(2x+3\right)}{5}-\frac{8}{15}\mid \cdot 15$  

${\left(4x-3\right)}^2-8+60x=3\cdot \left(-1\right)\left(2x+3\right)\left(2x+3\right)-8$  

$16x^2-24x+9-8+60x=-3{\left(2x+3\right)}^2-8$  

$16x^2+36x+1=-3\left(4x^2+12x+9\right)-8$  

$16x^2+36x+1=-12x^2-36x-27-8$  

$28x^2+72x+36=0\mid :4$  

$7x^2+18x+9=0$  

$\Delta ={18}^2-4\cdot 7\cdot 9=324-252=72$  

$\sqrt{\Delta }=\sqrt{72}=6\sqrt{2}$  

$x_1=\frac{-18-6\sqrt{2}}{2\cdot 7}=\frac{-18-6\sqrt{2}}{14}=\frac{-9-3\sqrt{2}}{7}$  

$x_2=\frac{-18+6\sqrt{2}}{2\cdot 7}=\frac{-18+6\sqrt{2}}{14}=\frac{-9+3\sqrt{2}}{7}$