To solve the expression $\frac{14 + 6\sqrt{5} + 7 - 3\sqrt{5}}{8}$, let's break it down step by step.

1. Combine like terms: $(14 + 7) + (6\sqrt{5} - 3\sqrt{5}) = 21 + 3\sqrt{5}$

2. Rewrite the expression: $\frac{21 + 3\sqrt{5}}{8}$

3. Separate the terms: $\frac{21}{8} + \frac{3\sqrt{5}}{8}$

So, the simplified result is: $\frac{21}{8} + \frac{3\sqrt{5}}{8}$

This is the final simplified form.

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