\(\Leftrightarrow x^2+3-\left(6x+1\right)\sqrt{x^2+3}+9x^2+3x-2=0\)
\(\Leftrightarrow x^2+3-\left(6x+1\right)\sqrt{x^2+3}+\left(3x+2\right)\left(3x-1\right)=0\)
\(\Leftrightarrow x^2+3-\left(3x+2+3x-1\right)\sqrt{x^2+3}+\left(3x+2\right)\left(3x-1\right)=0\)
\(\Leftrightarrow x^2+3-\left(3x+2\right)\sqrt{x^2+3}-\left(3x-1\right)\sqrt{x^2+3}+\left(3x+2\right)\left(3x-1\right)=0\)
\(\Leftrightarrow\sqrt{x^2+3}\left(\sqrt{x^2+3}-3x-2\right)-\left(3x-1\right)\left(\sqrt{x^2+3}-3x-2\right)=0\)
\(\Leftrightarrow\left(\sqrt{x^2+3}-3x+1\right)\left(\sqrt{x^2+3}-3x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x^2+3}=3x-1\left(x\ge\frac{1}{3}\right)\\\sqrt{x^2+3}=3x+2\left(x\ge-\frac{2}{3}\right)\end{matrix}\right.\) (1)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+3=\left(3x-1\right)^2\\x^2+3=\left(3x+2\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}8x^2-6x-2=0\\8x^2+12x+1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=-\frac{1}{4}\left(l\right)\\x=\frac{-3+\sqrt{7}}{4}\\x=\frac{-3-\sqrt{7}}{4}\left(l\right)\end{matrix}\right.\)
