Quadratic formula in double inequalities I have the double inequality: 
$-x^2 + x(2n+1) - 2n \leq u < -x^2 + x(2n-1)$ 
and I am trying to get it into the form
$x \leq \text{ anything } < x+1$ 
Or at least solve for x as the smallest term. I know I need to use the quadratic formula but I don't understand how I can solve for two quadratics at once? How would this work?

You don't solve two quadratics at once. You divide the double inequality into two separate ones:
$$-x^2+x(2n+1)-2n\le u$$
$$u<-x^2+x(2n-1)$$
From then on, you can use whatever method you want to isolate $x$. It looks like you already know how to do that. 
