\(5\cdot\left(x-2\right)^3-3\cdot\left(x-2\right)^3=250\)
\(\left(x-2\right)^3\cdot\left(5-3\right)=250\)
\(\left(x-2\right)^3\cdot2=250\)
\(\left(x-2\right)^3=\dfrac{250}{2}\)
\(\left(x-2\right)^3=125\)
\(\left(x-2\right)^3=5^3\)
\(x-2=5\)
\(x=5+2\)
\(x=7\)
\(5.\left(x-2\right)^3-3\left(x-2\right)^3=250\)
\(\Leftrightarrow\left(x-2\right)^3.\left(5-3\right)=250\)
\(\Leftrightarrow\left(x-2\right)^3.2=250\)
\(\Leftrightarrow\left(x-2\right)^3=125\)
\(\Leftrightarrow\left(x-2\right)^3=5^3\)
\(\Leftrightarrow x-2=5\)
\(\Leftrightarrow x=7\)