3.12: Intersection of a hyperbola and a line; length PQ

The curves $x^{2} - 4xy + 3y^{2} = 24$ and $y = 2x$ intersect at the points $P$ and $Q$. Find the coordinates of $P$ and $Q$.

Find the length of $PQ$. Give your answer in the form $a\sqrt{b}$ where $a$ is rational and $b$ is the smallest possible integer.