Найдем корень уравнения:
$$n + \frac{5}{14}n = 1\frac{1}{7}$$
$$\frac{14}{14}n + \frac{5}{14}n = \frac{8}{7}$$
$$\frac{19}{14}n = \frac{8}{7}$$
$$n = \frac{8}{7} : \frac{19}{14}$$
$$n = \frac{8}{7} \cdot \frac{14}{19}$$
$$n = \frac{8 \cdot 2}{19} = \frac{16}{19}$$
Ответ: $$\frac{16}{19}$$