\(8.6+288\div\left(x-3\right)^2=50\)
\(\Leftrightarrow\)\(48+288\div\left(x-3\right)^2=50\)
\(\Leftrightarrow\)\(288\div\left(x-3\right)^2=50-48\)
\(\Leftrightarrow\)\(288\div\left(x-3\right)^2=2\)
\(\Leftrightarrow\)\(\left(x-3\right)^2=288\div2\)
\(\Leftrightarrow\)\(\left(x-3\right)^2=144\)
\(\Leftrightarrow\)\(\left(x-3\right)^2=12^2\)
\(\Leftrightarrow\)\(x-3=12\)
\(\Leftrightarrow\)\(x=12+3\)
\(\Leftrightarrow\)\(x=15\)