$3x^2 + ax - 7 = 0$
$x^2_1 + x^2_2 = \frac{46}{9}$
$x_1 + x_2 = -\frac{a}{3}$
$x_1x_2 = -\frac{7}{3}$
$x^2_1 + x^2_2 = x^2_1 + x^2_2 + 2x_1x_2 - 2x_1x_2 = (x^2_1 + 2x_1x_2 + x^2_2) - 2x_1x_2 = (x_1 + x_2)^2 - 2x_1x_2 = \frac{46}{9}$
$(-\frac{a}{3})^2 - 2 * (-\frac{7}{3}) = \frac{46}{9}$
$\frac{a^2}{9} + \frac{14}{3} = \frac{46}{9}$ |* 9
$a^2 + 42 = 46$
$a^2 = 46 - 42$
$a^2 = 4$
a = ±2
Ответ: a = ±2