Решите уравнение: (2x+5)(x+2)=21.

Ответ:

\[(2x + 5)(x + 2) = 21\]

\[2x^{2} + 4x + 5x + 10 - 21 = 0\]

\[2x^{2} + 9x - 11 = 0\]

\[D = 9^{2} - 4 \cdot 2 \cdot ( - 11) =\]

\[= 81 + 88 = 169\]

\[x_{1} = \frac{- 9 + \sqrt{169}}{2 \cdot 2} = \frac{- 9 + 13}{4} =\]

\[= \frac{4}{4} = 1\]

\[x_{2} = \frac{- 9 - \sqrt{169}}{2 \cdot 2} = \frac{- 9 - 13}{4} =\]

\[= - \frac{22}{4} = - 5\frac{2}{4} = - 5,5\]

\[Ответ:x = 1;\ x = - 5,5.\]