ĐKXĐ: \(x\ge-\frac{1}{3}\)
\(\Leftrightarrow\sqrt{3x+1}-\sqrt{2x+3}-\frac{x-2}{4}=0\)
\(\Leftrightarrow\frac{x-2}{\sqrt{3x+1}+\sqrt{2x+3}}-\frac{x-2}{4}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\frac{1}{\sqrt{3x+1}+\sqrt{2x+3}}-\frac{1}{4}=0\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\Rightarrow x=2\\\sqrt{3x+1}+\sqrt{2x+3}=4\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow5x+4+2\sqrt{6x^2+11x+3}=16\)
\(\Leftrightarrow2\sqrt{6x^2+11x+3}=12-5x\) (\(x\le\frac{12}{5}\))
\(\Leftrightarrow4\left(6x^2+11x+3\right)=\left(12-5x\right)^2\)
\(\Leftrightarrow x^2-164x+132=0\) \(\Rightarrow\left[{}\begin{matrix}x=82+8\sqrt{103}\left(l\right)\\x=82-8\sqrt{103}\end{matrix}\right.\)
