1. **State the problem:** We are given the function $$f(x) = \frac{6x+5}{2-\sqrt{14+5x}}$$ and we want to understand its behavior and domain. 2. **Identify the domain restrictions:** The denominator cannot be zero and the expression inside the square root must be non-negative. 3. **Domain condition 1 (square root):** $$14 + 5x \geq 0 \implies 5x \geq -14 \implies x \geq -\frac{14}{5}$$ 4. **Domain condition 2 (denominator not zero):** $$2 - \sqrt{14 + 5x} \neq 0 \implies \sqrt{14 + 5x} \neq 2$$ 5. **Solve for when denominator is zero:** $$\sqrt{14 + 5x} = 2 \implies 14 + 5x = 4 \implies 5x = 4 - 14 = -10 \implies x = -2$$ 6. **Exclude $x = -2$ from the domain.** 7. **Final domain:** $$\left[-\frac{14}{5}, \infty \right) \setminus \{-2\}$$ 8. **Summary:** The function is defined for all $x$ greater or equal to $-\frac{14}{5}$ except at $x = -2$ where the denominator is zero. **Final answer:** The domain of $$f(x)$$ is $$\boxed{\left[-\frac{14}{5}, \infty \right) \setminus \{-2\}}$$.