$\begin{align}  & \text{4}\sqrt{x+2}-\sqrt{x+7}-5\sqrt{x-1}=0 \\ & \text{4}\sqrt{x+2}-\sqrt{x+7}=5\sqrt{x-1} \\ & \text{Square both sides} \\ & {{\left( \text{4}\sqrt{x+2}-\sqrt{x+7} \right)}^{2}}={{\left( 5\sqrt{x-1} \right)}^{2}} \\ & 16(x+2)-8\sqrt{({{x}^{2}}+9x+14)}+(x+7)=25(x-1) \\ & 17x+39-25x+25=8\sqrt{({{x}^{2}}+9x+14)} \\ & 64-8x=8\sqrt{({{x}^{2}}+9x+14)} \\ & 8-x=\sqrt{({{x}^{2}}+9x+14)} \\ & \text{Square both sides} \\ & 64-16x+{{x}^{2}}={{x}^{2}}+9x+14 \\ & 25x-50=0 \\ & x=\frac{50}{25}=2 \\\end{align}$