To solve the equation \(\frac{6}{5}x = 90\), follow these steps:
- Multiply both sides by the reciprocal of \(\frac{6}{5}\), which is \(\frac{5}{6}\):
\[ x = 90 \cdot \frac{5}{6} \]
- Calculate the right side:
\[ x = 90 \cdot \frac{5}{6} = \frac{90 \cdot 5}{6} = \frac{450}{6} = 75 \]
So, the solution is:
\[ x = 75 \]