The area enclosed by the curve $y = - 2 x ^ { 2 } + 3 x$ and the line $y = x$ is $\frac { q } { p }$. Find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]
The area enclosed by the curve $y = - 2 x ^ { 2 } + 3 x$ and the line $y = x$ is $\frac { q } { p }$. Find the value of $p + q$.\\
(Here, $p$ and $q$ are coprime natural numbers.) [4 points]