$x^2 - 0,5ax - 3a^2 = 0$
x = 2:
$2^2 - 0,5 * 2a - 3a^2 = 0$
$-3a^2 - a + 4 = 0$
$D = b^2 - 4ac = (-1)^2 - 4 * (-3) * 4 = 1 + 48 = 49 > 0$
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + \sqrt{49}}{2 * (-3)} = \frac{1 + 7}{-6} = \frac{8}{-6} = -\frac{4}{3} = -1\frac{1}{3}$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - \sqrt{49}}{2 * (-3)} = \frac{1 - 7}{-6} = \frac{-6}{-6} = 1$
Ответ: при $a = -1\frac{1}{3}$ и a = 1