1. Convert mixed numbers to improper fractions: \(\frac{15}{7}a + \frac{51}{14}a = \frac{78}{7} - \frac{22}{21} - \frac{31}{14}\).
2. Combine like terms: \(\frac{30a + 51a}{14} = \frac{234 - 44 - 105}{42}\) which simplifies to \(\frac{81a}{14} = \frac{85}{42}\).
3. Solve for a: \(a = \frac{85}{42} \times \frac{14}{81} = \frac{85}{3 \times 81} = \frac{85}{243}\).