Решите уравнение: (x+1)(x-2)-(4x-3)(x+5)=x(x-9).

\[- 4x^{2} - 9x + 13 = 0\]

\[4x^{2} + 9x - 13 = 0\]

\[D = 9^{2} - 4 \cdot 4 \cdot ( - 13) =\]

\[= 81 + 208 = 289\]

\[x_{1} = \frac{- 9 + \sqrt{289}}{2 \cdot 4} = \frac{- 9 + 17}{8} =\]

\[= \frac{8}{8} = 1\]

\[x_{2} = \frac{- 9 - \sqrt{289}}{2 \cdot 4} = \frac{- 9 - 17}{8} =\]

\[= \frac{- 26}{8} = - \frac{13}{4} = - 3\frac{1}{4}\]

\[Ответ:x = 1;\ x = - 3\frac{1}{4}.\]