Obel1x wrote: $\star$ Find all solutions to the equation: \[ \left(\left\lfloor x+\frac{7}{3} \right\rfloor \right)^2-\left\lfloor x-\frac{9}{4} \right\rfloor = 16 \] Let $x+\frac 73=y$ and the equation is $[y]^2-[y-\frac{55}{12}]=16$ $\iff$ $[y]^2-[y+\frac{5}{12}]=11$ and so $[y]$ and $[y+\frac{5}{12}]$ have different parity and the equation is : $n^2-(n+1)=11$ and $n=-3,4$ and so $y\in[-2-\frac 5{12},-2)\cup[5-\frac 5{12},5)$ And so $\boxed{x\in\left[-\frac{57}{12},-\frac{13}3\right)\cup\left[\frac{27}{12},\frac 83\right)}$