Найдем корень уравнения:
$$\frac{2}{7}c + \frac{2}{3}c - \frac{11}{21}c = 3\frac{1}{2}$$
$$\frac{6}{21}c + \frac{14}{21}c - \frac{11}{21}c = \frac{7}{2}$$
$$\frac{9}{21}c = \frac{7}{2}$$
$$c = \frac{7}{2} : \frac{9}{21}$$
$$c = \frac{7}{2} \cdot \frac{21}{9}$$
$$c = \frac{7 \cdot 7}{2 \cdot 3} = \frac{49}{6} = 8\frac{1}{6}$$
Ответ: $$8\frac{1}{6}$$