\(\sqrt{4x+20}+3\sqrt{x+5}-\sqrt{9x+45}=6\)
\(\Leftrightarrow\sqrt{4\left(x+5\right)}+3\sqrt{x+5}-\sqrt{9\left(x+5\right)}=6\)
\(\Leftrightarrow2\sqrt{x+5}+3\sqrt{x+5}-3\sqrt{x+5}=6\)
\(\Leftrightarrow2\sqrt{x+5}=6\)
\(\Leftrightarrow\sqrt{x+5}=3\)
\(\Leftrightarrow x+5=9\)
\(\Leftrightarrow x=4\)