1. **State the problem:** We need to find the derivative of the function $$f(x) = \frac{-x^{2} + 300x - 20000}{0.8}$$. 2. **Rewrite the function:** Since dividing by 0.8 is the same as multiplying by $\frac{1}{0.8} = 1.25$, we can write: $$f(x) = 1.25(-x^{2} + 300x - 20000)$$ 3. **Apply the derivative rule:** The derivative of a sum is the sum of the derivatives, and the derivative of $x^n$ is $nx^{n-1}$. 4. **Calculate the derivative:** $$f'(x) = 1.25 \times \frac{d}{dx}(-x^{2} + 300x - 20000)$$ $$= 1.25 \times (-2x + 300 + 0)$$ 5. **Simplify:** $$f'(x) = 1.25(-2x + 300) = 1.25 \times -2x + 1.25 \times 300$$ $$= -2.5x + 375$$ **Final answer:** $$f'(x) = -2.5x + 375$$