a) 5x2 - 11x + 2 = 0; б) 2p² + 7p - 30 = 0; в) 9у² - 30у + 25 = 0;

a) $$5x^2 - 11x + 2 = 0$$

a = 5, b = -11, c = 2

$$D = (-11)^2 - 4 \cdot 5 \cdot 2 = 121 - 40 = 81$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{11 + \sqrt{81}}{2 \cdot 5} = \frac{11 + 9}{10} = \frac{20}{10} = 2$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{11 - \sqrt{81}}{2 \cdot 5} = \frac{11 - 9}{10} = \frac{2}{10} = \frac{1}{5}$$

Ответ: $$x_1 = 2$$, $$x_2 = \frac{1}{5}$$

б) $$2p^2 + 7p - 30 = 0$$

a = 2, b = 7, c = -30

$$D = (7)^2 - 4 \cdot 2 \cdot (-30) = 49 + 240 = 289$$

$$p_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-7 + \sqrt{289}}{2 \cdot 2} = \frac{-7 + 17}{4} = \frac{10}{4} = \frac{5}{2} = 2.5$$

$$p_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-7 - \sqrt{289}}{2 \cdot 2} = \frac{-7 - 17}{4} = \frac{-24}{4} = -6$$

Ответ: $$p_1 = 2.5$$, $$p_2 = -6$$

в) $$9y^2 - 30y + 25 = 0$$

a = 9, b = -30, c = 25

$$D = (-30)^2 - 4 \cdot 9 \cdot 25 = 900 - 900 = 0$$

$$y = \frac{-b}{2a} = \frac{30}{2 \cdot 9} = \frac{30}{18} = \frac{5}{3}$$

Ответ: $$y = \frac{5}{3}$$