Подставим $$s=\frac{12}{17}$$ в выражение $$-s(1-s) - (9-s)^2$$:
$$\frac{-12}{17}(1-\frac{12}{17}) - (9-\frac{12}{17})^2 = \frac{-12}{17}(\frac{17-12}{17}) - (\frac{153-12}{17})^2 = \frac{-12}{17}(\frac{5}{17}) - (\frac{141}{17})^2 = \frac{-60}{289} - \frac{19881}{289} = \frac{-19941}{289}$$
Ответ: $$\frac{-19941}{289}$$