Not calculus this time

Algebra Level 5

\[\large \lfloor 4x\rfloor +\lceil x\rceil =x^{2}+4\]Find 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.