10.3. Find the greatest solution of the inequality

$$
\frac{-\log _{3}(100+2 x \sqrt{2 x+25})^{3}+\left|\log _{3} \frac{100+2 x \sqrt{2 x+25}}{\left(x^{2}+2 x+4\right)^{4}}\right|}{3 \log _{6}(50+2 x \sqrt{2 x+25})-2 \log _{3}(100+2 x \sqrt{2 x+25})} \geqslant 0
$$
Answer. $12+4 \sqrt{3} \approx 18.93$.