Решение:

$f \left(x\right) = ax^{2} + bx + c ; c = 0$
 $g \left(x\right) = kx ; k = 3$
при $x = 3 , y = 4$
$\left\{\begin{matrix} a \cdot 3^{2} + b \cdot 3 = 0 \\ a \cdot 4^{2} + b \cdot 4 = 4 \end{matrix}\right.$
$\left\{\begin{matrix} 9 a + 3 b = 0 \\ 16 a + 4 b = 4 \end{matrix}\right.$
$\left\{\begin{matrix} 3 a + b = 0 \\ 4 a + b = 1 \end{matrix}\right.$
$\left\{\begin{matrix} b = - 3 a \\ 4 a + \left(- 3 a\right) = 1 . \end{matrix}\right.$
$a = 1 \Rightarrow b = - 3 \cdot 1 = - 3$
$a = 1$ и $b = - 3$
$x^{2} - 3 x = 3 x$
$x^{2} - 6 x = 0$
$x \left(x - 6\right) = 0$
$x = 0 , x = 6 .$

Ответ: 6

Источник: ФИПИ