$\frac{3x+4y}{xy}=\frac{xy-90}{6y}\text{ and }\frac{xy-90}{6y}=8$

$\left\{\begin{matrix}x=2\sqrt{5154}+144\text{, }&y=\frac{3\sqrt{5154}}{190}-\frac{72}{95}\\x=144-2\sqrt{5154}\text{, }&y=-\frac{3\sqrt{5154}}{190}-\frac{72}{95}\end{matrix}\right.$

$\left\{\begin{matrix}y=-\frac{3\sqrt{5154}}{190}-\frac{72}{95}\text{, }&x=144-2\sqrt{5154}\\y=\frac{3\sqrt{5154}}{190}-\frac{72}{95}\text{, }&x=2\sqrt{5154}+144\end{matrix}\right.$