An algebra problem by Aly Ahmed

By checking the options and assuming x to be integer, i found this solution. Waiting for someone to show this for a rational $x$ as well

Assuming $x$ to be an integer:

\[\begin{align} \lfloor x^2 \rfloor + \lceil 2x \rceil &= 3 \\ x^2 + 2x &= 3 \quad [\text{No fractional part remains}] \\ x^2 + 2x -3 &= 0
\\ (x-1)(x+3) &= 0 \\ x &= \boxed{1, -3}

\end{align}\]