Final answer:
To solve the equation, simplify the expression and cross multiply to eliminate the fractions. Then, rearrange the equation in standard form and solve for x using numerical methods.
Step-by-step explanation:
To solve the equation, we can start by simplifying the expression. Combining like terms, we have:
(1.9x^2.8) / x^2 = (2.8x^3.2) / (0.5 - x)^2
Next, we can cross multiply to eliminate the fractions:
(1.9x^2.8)(0.5 - x)^2 = (2.8x^3.2)(x^2)
After expanding and simplifying both sides, we have a polynomial equation. Rearranging it in standard form, we get:
1.9(0.5 - x)^2x^2 - 2.8x^3.2x^2 = 0
Simplifying further, we obtain:
0.95(1 - 2x + x^2)x^2 - 2.8x^5.2 = 0
From here, we can solve for x using numerical methods, such as graphing or using a calculator or computer program that can handle polynomial equations.