(i) The given equation is $2 x^{2}-8 x+5=0$
This is of the form $a x^{2}+b x+c=0$, where $a=2, b=-8$ and $c=5$.
$\therefore$ Discriminant,
$D=b^{2}-4 a c=(-8)^{2}-4 \times 2 \times 5=64-40=24>0$
Hence, the given equation has real and unequal roots.

(ii) The given equation is $3 x^{2}-2 \sqrt{6} x+2=0$.
This is of the form $a x^{2}+b x+c=0$, where $a=3, b=-2 \sqrt{6}$ and $c=2$.
$\therefore$ Discriminant, $D=b^{2}-4 a c=(-2 \sqrt{6})^{2}-4 \times 3 \times 2=24-24=0$
Hence, the given equation has real and equal roots.