Check the picture below.
[tex]\textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ w=3L+7\\ A=48 \end{cases}\implies 48=L(3L+7)\implies 48=3L^2+7L \\\\\\ 0=3L^2+7L-48\implies 0=(3L+16)(L-3) \\\\[-0.35em] ~\dotfill\\\\ 0=3L+16\implies -16=3L\implies -\cfrac{16}{3}=L \\\\[-0.35em] ~\dotfill\\\\ 0=L-3\implies 3=L~~\textit{\Large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ w=3L+7\implies w=3(3)+7\implies w=16[/tex]
notice, we didn't use the negative value of "L", because the length can't be negative.
