$\large x-2 = \sqrt{4-3\sqrt{4-3\sqrt{10-3x}}} \quad,\quad x= \, ?$

The answer is 3.

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It can be seen that $x-2$ must be positive, as $\sqrt{n}$ returns a positive value or zero. Therefore $x>=2$ . And $10-3x>=0$ to avoid imaginary numbers and must be a perfect square. From this, $x$ must be 1, 2, or 3. Of these, only $\boxed{3}$ satisfies all conditions.