Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

Explanation

To solve the problem, we need to find a natural number \( x \) such that the square of the number diminished by 84 is equal to thrice of 8 more than the number.

### Step-by-Step Solution:

1. **Set up the equation**:
We start by translating the problem into a mathematical equation. The statement "the square of a natural number diminished by 84" can be expressed as \( x^2 - 84 \). The phrase "thrice of 8 more than the given number" translates to \( 3(x + 8) \). Therefore, we can set up the equation:
\[
x^2 - 84 = 3(x + 8)
...