\(\sqrt{x}+9=5-\sqrt{2x}+4\)
<=> \(\sqrt{x}+\sqrt{2x}=5+4-9\)
<=> \(\sqrt{x}+4\sqrt{x}=0\)
<=> \(5\sqrt{x}=0\)
<=> \(\sqrt{x}=0\)
<=> \(x=0\)
\(\Leftrightarrow\sqrt{x}+\sqrt{2x}=5+4-9\Leftrightarrow\sqrt{x}\left(1+\sqrt{2}\right)=0\Leftrightarrow x=0\)