To solve the equation, we can start by simplifying both sides:

5/x + 3 + 20x/(9 - x²) = 10/(3 - x)

To simplify the right side, we can multiply both the numerator and denominator by -1:

5/x + 3 + 20x/(9 - x²) = -10/(x - 3)

Now, let's find a common denominator for the fractions on the left side. The common denominator is x(9 - x²):

(5(9 - x²) + 3x(9 - x²) + 20x) / (x(9 - x²)) = -10/(x - 3)

Simplifying the numerator:

(45 - 5x² + 27x - 3x³ + 20x) / (x(9 - x²)) = -10/(x - 3)

Combining like terms:

(-3x³ + 47x + 45) / (x(9 - x²)) = -10/(x - 3)

Now, let's multiply both sides by (x - 3) to eliminate the denominator on the right side:

(-3x³ + 47x + 45) / (9 - x²) = -10

Multiplying both sides by (9 - x²):

(-3x³ + 47x + 45) = -10(9 - x²)

Expanding the right side:

-3x³ + 47x + 45 = -90 + 10x²

Rearranging the equation:

3x³ - 10x² + 47x + 45 + 90 = 0

Combining like terms:

3x³ - 10x² + 47x + 135 = 0

Unfortunately, this equation cannot be easily factored or solved algebraically. We may need to use numerical methods or a graphing calculator to approximate the solutions.