Find the roots of the quadratic equation $6x^{2}-x-2=0$.

(A) We have the quadratic equation $6x^{2}-x-2=0$.
To find the roots,we factorize the quadratic expression by splitting the middle term:
$6x^{2}-x-2 = 6x^{2}+3x-4x-2$
Grouping the terms,we get:
$= 3x(2x+1)-2(2x+1)$
$= (3x-2)(2x+1)$
The roots of $6x^{2}-x-2=0$ are the values of $x$ for which $(3x-2)(2x+1)=0$.
Setting each factor to zero:
$3x-2=0$ or $2x+1=0$
Solving for $x$:
$3x=2 \implies x=\frac{2}{3}$
$2x=-1 \implies x=-\frac{1}{2}$
Therefore,the roots of the quadratic equation are $\frac{2}{3}$ and $-\frac{1}{2}$.