How would one solve an equation with a floor function in it:
$$a - (2x + 1)\left\lfloor{\frac {a - 2x(x + 1)}{2x + 1}}\right\rfloor - 2x(x + 1) = 0$$
$a$ is a given and can be treated as a natural number, and all $x$ other than integers can be discarded. At least one non-trivial solution would be sufficient.
Maybe an algorithmic method could be used?