SAT Question 58dcc59f: Nonlinear Functions answer and explanation with Desmos solution

Let $w$ represent the width of the rectangular garden, in feet. Since the length of the garden will be $5$ feet longer than the width of the garden, the length of the garden will be $w+5$ feet. Thus the area of the garden will be $w\times (w+5)$. It is also given that the area of the garden will be $104$ square feet. Therefore, $w\times (w+5)=104$, which is equivalent to $w^2+5w-104=0$. Factoring this equation results in $(w+13)\times (w-8)=0$. Therefore, $w=8$ and $w=-13$. Because width cannot be negative, the width of the garden must be $8$ feet. This means the length of the garden must be $8+5=13$ feet.