\(\sqrt{x+1}+\sqrt{4x+4}=6\)
\(\Leftrightarrow\sqrt{x+1}+4\sqrt{x+1}=6\)
\(\Leftrightarrow5\sqrt{x+1}=6\)
\(\Leftrightarrow\sqrt{x+1}=\dfrac{6}{5}\)
\(\Leftrightarrow x+1=\left(\dfrac{6}{5}\right)^2\)
\(\Leftrightarrow x+1=\dfrac{36}{25}\)
`<=> x= 11/25`