1. Multiply both sides of the equation by v-1/5 to get rid of the denominator.
2v=8/(v-1/5)
2v(v-1/5)=(8/(v-1/5))(v-1/5)
2v(v-1/5)=(8/(color(red)cancelcolor(black)(v-1/5)))(color(red)cancelcolor(black)(v-1/5))
color(orange)(2v)(color(blue)v-color(purple)(1/5))=8
2. Use the distributive property, color(orange)a(color(blue)b+color(purple)c)=color(orange)acolor(blue)b+color(orange)acolor(purple)c, to expand the left side of the equation.
color(orange)(2v)(color(blue)(v))+color(orange)(2v)(color(purple)(-1/5))=8
2v^2-(2v)/5=8
3. Multiply the whole equation by 5 to get rid of the denominator.
5(2v^2-(2v)/5)=5(8)
10v^2-2v=40
4. Subtract 40 from both sides.
10v^2-2v-40=0
5. Factor out 2 from the left side of the equation.
2(color(teal)5v^2 color(violet)(-1)v color(brown)(-20))=0
6. Use the quadratic formula to factor the trinomial.
color(teal)(a=5)color(white)(XXXXX)color(violet)(b=-1)color(white)(XXXXX)color(brown)(c=-20)
v=(-b+-sqrt(b^2-4ac))/(2a)
v=(-(color(violet)(-1))+-sqrt((color(violet)(-1))^2-4(color(teal)5)(color(brown)(-20))))/(2(color(teal)5))
color(green)(|bar(ul(color(white)(a/a)v=(1+-sqrt(401))/10color(white)(a/a)|)))
