ĐKXĐ: \(x\ge3\)
\(\Leftrightarrow\sqrt{x+4}=\sqrt{2x-6}+1\)
\(\Leftrightarrow x+4=2x-5+2\sqrt{2x-6}\)
\(\Leftrightarrow9-x=2\sqrt{2x-6}\) (\(x\le9\))
\(\Leftrightarrow\left(9-x\right)^2=4\left(2x-6\right)\)
\(\Leftrightarrow x^2-18x+81=8x-24\)
\(\Leftrightarrow x^2-26x+105=0\)
\(\Rightarrow\left[{}\begin{matrix}x=21>9\left(l\right)\\x=5\end{matrix}\right.\)