(i) The given equation is $5 x^{2}-4 x+1=0$
This is of the form $a x^{2}+b x+c=0$, where $a=5, b=-4$ and $c=1$.
$\therefore$ Discriminant,
$D=b^{2}-4 a c=(-4)^{2}-4 \times 5 \times 1=16-20=-4<0$
Hence, the given equation has no real roots.

(ii) The given equation is
$\begin{array}{l}
5 x(x-2)+6=0 \\
\Rightarrow 5 x^{2}-10 x+6=0
\end{array}$
This is of the form $a x^{2}+b x+c=0$, where $a=5, b=-10$ and $c=6$.
$\therefore$ Discriminant,
$D=b^{2}-4 a c=(-10)^{2}-4 \times 5 \times 6=100-120=-20<0$
Hence, the given equation has no real roots.