$9.282 \sqrt{3 x^{2}+5 x+7}-\sqrt{3 x^{2}+5 x+2}>1$.
## Solution.

$$
\begin{aligned}
& \sqrt{3 x^{2}+5 x+7}>1+\sqrt{3 x^{2}+5 x+2} \Leftrightarrow \\
& \Leftrightarrow 3 x^{2}+5 x+7>1+2 \sqrt{3 x^{2}+5 x+2}+3 x^{2}+5 x+2 \Leftrightarrow
\end{aligned}
$$

$$
\Leftrightarrow \sqrt{3 x^{2}+5 x+2}<2 \Leftrightarrow\left\{\begin{array} { l } 
{ 3 x ^ { 2 } + 5 x + 2 < 4 , } \\
{ 3 x ^ { 2 } + 5 x + 2 \geq 0 }
\end{array} \Leftrightarrow \left\{\begin{array} { l } 
{ ( x + 2 ) ( x - \frac { 1 } { 3 } ) < 0 , } \\
{ ( x + 1 ) ( x + \frac { 2 } { 3 } ) \geq 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
-2<x<\frac{1}{3} \\
{\left[\begin{array}{l}
x \geq-\frac{2}{3} \\
x \leq-1
\end{array}\right.}
\end{array}\right.\right.\right.
$$

Answer: $\quad x \in(-2 ;-1] \cup\left[-\frac{2}{3} ; \frac{1}{3}\right)$.