The area is given by the function:
[tex]A=8x^2+14x-15[/tex]The length is 2x+5 so factorize the above function as follows:
[tex]\begin{gathered} A=8x^2+14x-15 \\ A=8x^2+20x-6x-15 \\ A=4x(2x+5)-3(2x_{}+5) \\ A=(4x-3)(2x+5) \end{gathered}[/tex]Since the length is 2x+5, therefore the width is 4x-3.
Hence the width of the rectangle is 4x-3.