$\left(1\right)2x^{2}-3=8x$，
$2x^{2}-8x=3$，
${x}^{2}-4x=\frac{3}{2}$，
${x}^{2}-4x+4=\frac{3}{2}+4$，
${(x-2)}^{2}=\frac{11}{2}$，
$x-2=±\frac{\sqrt{22}}{2}$，
$\therefore {x}_{1}=2+\frac{\sqrt{22}}{2}，{x}_{2}=2-\frac{\sqrt{22}}{2}$；
$(2)5x^{2}=4-2x$，
$5x^{2}+2x-4=0$，
$a=5$，$b=2$，$c=-4$，
$b^{2}-4ac=2^{2}-4\times 5\times \left(-4\right)=84 \gt 0$，
$\therefore x=\frac{-2±\sqrt{84}}{2×5}$，
$\therefore {x}_{1}=\frac{-1+\sqrt{21}}{5}，{x}_{2}=\frac{-1-\sqrt{21}}{5}$；
$(3)2y^{2}-y=2\left(1-2y\right)$，
$y\left(2y-1\right)+2\left(2y-1\right)=0$，
$(2y-1)\left(2+y\right)=0$，
$2y-1=0$或$2+y=0$，
$\therefore {y}_{1}=\frac{1}{2}，{y}_{2}=-2$.

$\left(1\right)2x^{2}-3=8x$，
$2x^{2}-8x=3$，
${x}^{2}-4x=\frac{3}{2}$，
${x}^{2}-4x+4=\frac{3}{2}+4$，
${(x-2)}^{2}=\frac{11}{2}$，
$x-2=±\frac{\sqrt{22}}{2}$，
$\therefore {x}_{1}=2+\frac{\sqrt{22}}{2}，{x}_{2}=2-\frac{\sqrt{22}}{2}$；
$(2)5x^{2}=4-2x$，
$5x^{2}+2x-4=0$，
$a=5$，$b=2$，$c=-4$，
$b^{2}-4ac=2^{2}-4\times 5\times \left(-4\right)=84 \gt 0$，
$\therefore x=\frac{-2±\sqrt{84}}{2×5}$，
$\therefore {x}_{1}=\frac{-1+\sqrt{21}}{5}，{x}_{2}=\frac{-1-\sqrt{21}}{5}$；
$(3)2y^{2}-y=2\left(1-2y\right)$，
$y\left(2y-1\right)+2\left(2y-1\right)=0$，
$(2y-1)\left(2+y\right)=0$，
$2y-1=0$或$2+y=0$，
$\therefore {y}_{1}=\frac{1}{2}，{y}_{2}=-2$.