a person wishes to build a rectangular fence that will enclose an area of 317 square feet. the width of the fence is to be 3 feet less that

Let  W = 2L - 3  .....    so we have

(2L - 3)(L) = 317       simplify

2L² - 3L = 317           subtract 317 from both sides

2L² - 3L - 317  = 0      using the onsite calculator and subbing x for L, we have

$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{317}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{2\,545}}}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}{{\mathtt{4}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{2\,545}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{{\mathtt{4}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{11.861\: \!998\: \!255\: \!629\: \!438\: \!5}}\\
{\mathtt{x}} = {\mathtt{13.361\: \!998\: \!255\: \!629\: \!438\: \!5}}\\
\end{array} \right\}$$

So...L =  13.4 ft

And W = 2(13.4) - 3 =  23.8 ft