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

\[- 2x^{2} + 3x + 9 = 0\]

\[2x^{2} - 3x - 9 = 0\]

\[D = ( - 3)^{2} - 4 \cdot 2 \cdot ( - 9) =\]

\[= 9 + 72 = 81\]

\[x_{1} = \frac{- ( - 3) + \sqrt{81}}{2 \cdot 2} = \frac{3 + 9}{4} =\]

\[= \frac{12}{4} = 3\]

\[x_{2} = \frac{- ( - 3) - \sqrt{81}}{2 \cdot 2} = \frac{3 - 9}{4} =\]

\[= \frac{- 6}{4} = - \frac{3}{2} = - 1\frac{1}{2}\]

\[Ответ:\ \ x = 3;\ x = - 1,5.\]