6.163. $5 \sqrt[15]{x^{22}}+\sqrt[15]{x^{14} \cdot \sqrt{x}}-22 \sqrt[15]{x^{7}}=0$.
## Solution.

Domain of definition: $x \geq 0$.

From the condition $5 x^{\frac{22}{15}}+x^{\frac{27}{30}}-22 x^{\frac{7}{15}}=0 \Leftrightarrow 5 x^{\frac{44}{30}}+x^{\frac{27}{30}}-22 x^{\frac{14}{30}}=0 \Leftrightarrow$ $\Leftrightarrow x^{\frac{14}{30}}\left(5 x+x^{\frac{1}{2}}-22\right)=0$. Then $x^{\frac{14}{30}}=0, x_{1}=0$ or $5 x+x^{\frac{1}{2}}-22=0$.

Let $x^{\frac{1}{2}}=y \geq 0$. The equation in terms of $y$ becomes
$5 y^{2}+y-22=0$, from which $y_{1}=-\frac{11}{5}, y_{2}=2 ; y_{1}=-\frac{11}{5}<0$ is not valid. Then $x_{2}^{\frac{1}{2}}=2, x_{2}=4$

Answer: $x_{1}=0, x_{2}=4$