Not calculus this time

Algebra Level 5

4x+x=x2+4\large \lfloor 4x\rfloor +\lceil x\rceil =x^{2}+4Find the sum of squares of the solutions to the above equation.

Notations: \lfloor \cdot \rfloor denotes the floor function and \lceil \cdot \rceil denotes the ceiling function.

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