\(\sqrt{4x+6}=x+2\left(x\ge-\dfrac{3}{2}\right)\)
\(\Leftrightarrow\left|4x+6\right|=\left(x+2\right)^2\)
\(\Leftrightarrow4x+6=x^2+4x+4\)
\(\Leftrightarrow x^2-2=0\)
\(\Leftrightarrow\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\sqrt{2}=0\\x-\sqrt{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\sqrt{2}\left(tm\right)\\x=\sqrt{2}\left(tm\right)\end{matrix}\right.\)
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