To solve the equation \( x^2 = \frac{36}{169} \) by inspection, we can take the square root of both sides.
Starting with:
\[ x^2 = \frac{36}{169} \]
Taking the square root, we get:
\[ x = \pm \sqrt{\frac{36}{169}} \]
Calculating the square root:
\[ \sqrt{\frac{36}{169}} = \frac{\sqrt{36}}{\sqrt{169}} = \frac{6}{13} \]
Thus, we have:
\[ x = \frac{6}{13} \quad \text{or} \quad x = -\frac{6}{13} \]
This gives us the solution set:
\[ \left{-\frac{6}{13}, \frac{6}{13}\right} \]
So, the correct solution set from the options provided is:
C. \({-6/13, 6/13}\)