What is the largest value of $x$ such that $(4x+11)(2x-8)=x(2x+7)$? Express your answer as a fraction.
We expand both sides: \begin{align*}
(4x+11)(2x-8)&= x(2x+7)\\
8x^2-10x-88 &= 2x^2 + 7x\\
6x^2-17x-88 &= 0\\
(2x-11)(3x+8) &= 0
\end{align*}Therefore, the smaller of the two solutions is $x=-8/3$ and the larger is $x=\boxed{\frac{11}{2}}$