G3.1 Given that the solution of the equation $\sqrt{3 x+1}+\sqrt{3 x+6}=\sqrt{4 x-2}+\sqrt{4 x+3}$ is $a$, find the value of $a$.
$\begin{array}{l}\sqrt{3 x+6}-\sqrt{4 x-2}=\sqrt{4 x+3}-\sqrt{3 x+1} \\ (\sqrt{3 x+6}-\sqrt{4 x-2})^{2}=(\sqrt{4 x+3}-\sqrt{3 x+1})^{2} \\ 3 x+6+4 x-2-2 \sqrt{12 x^{2}+18 x-12}=4 x+3+3 x+1-2 \sqrt{12 x^{2}+13 x+3} \\ \sqrt{12 x^{2}+18 x-12}=\sqrt{12 x^{2}+13 x+3} \\ 12 x^{2}+18 x-12=12 x^{2}+13 x+3 \\ x=3\end{array}$