We are given the equation:

$1.32 \left( 1932.69 + \left( 83.33x + 3.74x^2 \right) \left( \frac{x}{3} \right) \left( \frac{83.33}{83.33 + 83.33 + 7.471x} \right) \right) = 4549.23 + \left( 715.24x + 91.6x^2 \right) \left( \frac{x}{3} \right) \left( \frac{715.24}{715.24 \cdot 2 + 18.325x} \right)$

Step-by-Step Approach:

1. Simplify the expression on both sides of the equation.

   On the left-hand side: $1.32 \left( 1932.69 + \left( 83.33x + 3.74x^2 \right) \left( \frac{x}{3} \right) \left( \frac{83.33}{166.66 + 7.471x} \right) \right)$

   On the right-hand side: $4549.23 + \left( 715.24x + 91.6x^2 \right) \left( \frac{x}{3} \right) \left( \frac{715.24}{1430.48 + 18.325x} \right)$

2. Expand the terms where possible. It will help simplify the expression into a solvable form.

3. Isolate terms involving $x$ on both sides and solve for $x$.

The equation looks quite complex due to the nonlinear terms involving $x^2$, $x$, and fractions. To solve this equation, we could approach it numerically or using algebraic simplification techniques.

Let me know if you'd like to go through the detailed steps for simplification, or if you'd like me to proceed with finding the solution numerically!