I propose this solution, check it out!
We must find solution on the positive real axis.
Let be x= n + \delta, where n is the integer part and \delta is the fractional part with 0 \leq \delta < 1.
Given that x \lfloor x \lfloor x \rfloor \rfloor=82 and x \lfloor x \lfloor x \rfloor \rfloor...