№1. Решите уравнение: a) $$6x^2 - 3x = 0$$; б) $$25x^2 = 81$$; в) $$3x^2 - 7x - 6 = 0$$.

a) $$6x^2 - 3x = 0$$ $$3x(2x - 1) = 0$$ $$3x = 0$$ или $$2x - 1 = 0$$ $$x_1 = 0$$ или $$x_2 = \frac{1}{2}$$ Ответ: $$x_1 = 0, x_2 = \frac{1}{2}$$ б) $$25x^2 = 81$$ $$x^2 = \frac{81}{25}$$ $$x = \pm \sqrt{\frac{81}{25}}$$ $$x_1 = \frac{9}{5}$$ или $$x_2 = -\frac{9}{5}$$ Ответ: $$x_1 = \frac{9}{5}, x_2 = -\frac{9}{5}$$ в) $$3x^2 - 7x - 6 = 0$$ $$D = (-7)^2 - 4 \cdot 3 \cdot (-6) = 49 + 72 = 121$$ $$x_{1,2} = \frac{-(-7) \pm \sqrt{121}}{2 \cdot 3} = \frac{7 \pm 11}{6}$$ $$x_1 = \frac{7 + 11}{6} = \frac{18}{6} = 3$$ $$x_2 = \frac{7 - 11}{6} = \frac{-4}{6} = -\frac{2}{3}$$ Ответ: $$x_1 = 3, x_2 = -\frac{2}{3}$$