7. Найдите корни уравнения: a) 10x2 – 3x – 0,4 = 0; B) 3x2 - 4x + 2 = 0; д) 7у² + 5y = 2;

1. a) $$10x^2 - 3x - 0.4 = 0$$
   $$10x^2 - 3x - \frac{2}{5} = 0$$
   $$50x^2 - 15x - 2 = 0$$
   $$D = (-15)^2 - 4(50)(-2) = 225 + 400 = 625$$
   $$x = \frac{15 \pm \sqrt{625}}{2(50)} = \frac{15 \pm 25}{100}$$
   $$x_1 = \frac{15 + 25}{100} = \frac{40}{100} = 0.4$$
   $$x_2 = \frac{15 - 25}{100} = \frac{-10}{100} = -0.1$$
2. в) $$3x^2 - 4x + 2 = 0$$
   $$D = (-4)^2 - 4(3)(2) = 16 - 24 = -8$$
   $$D < 0$$, уравнение не имеет корней.
3. д) $$7y^2 + 5y = 2$$
   $$7y^2 + 5y - 2 = 0$$
   $$D = 5^2 - 4(7)(-2) = 25 + 56 = 81$$
   $$y = \frac{-5 \pm \sqrt{81}}{2(7)} = \frac{-5 \pm 9}{14}$$
   $$y_1 = \frac{-5 + 9}{14} = \frac{4}{14} = \frac{2}{7}$$
   $$y_2 = \frac{-5 - 9}{14} = \frac{-14}{14} = -1$$

Ответ: a) x = 0.4, x = -0.1; B) нет корней; д) y = 2/7, y = -1