It is a equation with the form of
$$ y[n] - \rho y[n-2] = x[n] ,\qquad y^2 - \rho = 0 $$
I am trying to find similar equations to this as I do not understand how to solve it, but I am not too sure what I am looking for. For context my professor calls equations in square brackets as discrete systems/equations but when I try searching it up on google nothing similar shows up. More or less, I just want to understand how the second step is achieved. Any help regarding this would be greatly appreciated.