\(\frac{180}{v}+\frac{180}{v-5}=\frac{8}{5}\)
\(900\left(v-5\right)+900v=8v\left(v-5\right)\)
\(1800v-4500=8v^2-40v\)
\(1800v-4500-8v^2+40v=0\)
\(1840v-4500-8v^2=0\)
\(\left[{}\begin{matrix}v=-\frac{-1840+\sqrt{1840^2-144000}}{16}\\v=-\frac{-1840-\sqrt{1840^2-144000}}{16}\end{matrix}\right.\)