Answer
$x\approx 1930.59 $.
Work Step by Step
Given \begin{equation}
\sqrt[7]{145 x}=6
\end{equation} Start by rewriting the radical as a power of fraction and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[7]{145 x}&=6\\
\left(145 x\right)^{\frac{1}{7}}&= 6\\
\left(\left(145 x\right)^{\frac{1}{7}}\right)^7& = \left( 6\right)^7 \\
145 x& =6^7\\
x&= \frac{6^7}{145}\\
& \approx 1930.59.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\left(145 \cdot \frac{6^7}{145}\right)^{\frac{1}{7}}&\stackrel{?}{=}6\\
6& =6\quad \checkmark.
\end{aligned}
\end{equation} The solution is $x\approx 1930.59 $.
