\(\frac{x+4}{20}=\frac{5}{x+4}\)
=> \(\left(x+4\right)\left(x+4\right)=20\cdot5\)
=> \(\left(x+4\right)^2=100\)
=> \(\left(x+4\right)^2=\left(\pm10\right)^2\)
=> \(\orbr{\begin{cases}x+4=10\\x+4=-10\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\\x=-14\end{cases}}\)