Let's break down the expression step by step:

1. Calculate \(6^2\):
\[
6^2 = 36
\]

2. Calculate \(5^2\):
\[
5^2 = 25
\]

3. Substitute these values back into the expression:
\[
\frac{36}{43} + 2 \times 25
\]

4. Perform the multiplication:
\[
2 \times 25 = 50
\]

5. Substitute this value back into the expression:
\[
\frac{36}{43} + 50
\]

6. Add the fraction and the integer:
\[
\frac{36}{43} + 50
\]

Since \(\frac{36}{43}\) is a fraction and 50 is an integer, the final answer can be written as a mixed number or left as is:
\[
50 + \frac{36}{43}
\]

So, the final result is:
\[
50 + \frac{36}{43}
\]

Or, if you prefer a decimal approximation:
\[
50 + \frac{36}{43} \approx 50.8372
\]