9.197. $x^{2}(x+3 \sqrt{5})+5(3 x+\sqrt{5})>0$.
## Solution.

From the condition

$$
x^{3}+3 \sqrt{5} x^{2}+15 x+5 \sqrt{5}>0 \Leftrightarrow(x+\sqrt{5})^{3}>0, x+\sqrt{5}>0, x>-\sqrt{5}
$$

Answer: $x \in(-\sqrt{5} ; \infty)$.