A word problem about a rectangular carpet 

Let $x$ be the length of the carpet and $y$ be its width. Then the area of the carpet is 
\[(1)      xy=108.\]
Also 
\[      x=y+3.\]
Substituting $x$ in terms of $y$ in equation (1) we get 
\[(y+3)y=108      \Rightarrow    y^2+3y-108=0.\]
Using quadratic formula we get
\[y=\frac{-3\pm \sqrt{9+4 \times 108}}{2}=\frac{-3 \pm \sqrt{441}}{2}=\frac{-3 \pm 21}{2}.\]
Hence $y=9$ or $y=-12$. The solution $y=-12$ is not acceptable, so the width of the carpet must be $y=9$, and the length is $x=9+3=12$.