An algebra problem [Romania 1974]

Algebra Level 2

$\large \sqrt{a+bx} + \sqrt{b+cx} + \sqrt{c+ax} = \sqrt{b-ax} + \sqrt{c-bx} +\sqrt{a-cx}$

Let $$a,b$$ and $$c$$ be real and positive parameters. Solve the equation above. What is the value of $$x$$?

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