2. Решить уравнение: $$2x^2 – 7x - 9 =0$$

$$\begin{aligned} 2x^2 - 7x - 9 &= 0 \\D &= b^2 - 4ac = (-7)^2 - 4 \cdot 2 \cdot (-9) = 49 + 72 = 121 \\x_1 &= \frac{-b + \sqrt{D}}{2a} = \frac{7 + \sqrt{121}}{2 \cdot 2} = \frac{7 + 11}{4} = \frac{18}{4} = \frac{9}{2} = 4.5 \\x_2 &= \frac{-b - \sqrt{D}}{2a} = \frac{7 - \sqrt{121}}{2 \cdot 2} = \frac{7 - 11}{4} = \frac{-4}{4} = -1 \end{aligned}$$ Ответ: $$\boxed{x_1 = 4.5, x_2 = -1}$$