27. Find all real solutions of the equation

$$
\begin{aligned}
& \sqrt{a+b x}+\sqrt{b+c x}+\sqrt{c+a x}= \\
& =\sqrt{b-a x}+\sqrt{c-b x}+\sqrt{a-c x}
\end{aligned}
$$

if it is known that it has solutions.
76.27. Answer. If the numbers $a, b, c$ are non-negative and at least one of them is not zero, then $x=0$. If $a=b=c=0$, then $x$ is any real number. Other options are not possible if it is known that the equation has a solution.