Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

The given equation is $3 x^{2}-2 x+2=0$.

Comparing it with $a x^{2}+b x+c=0$, we get

$a=3, b=-2$ and $c=2$

$\therefore$ Discriminant, $D=b^{2}-4 a c=(-2)^{2}-4 \times 3 \times 2=4-24=-20<0$

Hence, the given equation has no real roots (or real roots does not exist).