# How do I use the quadratic formula to solve #2 + 5/(r-1) = 12/((r-1)^2)#?

##### 1 Answer

Aug 22, 2014

The answers are

You may be tempted to expand

#r=y+1#

We have an NPV:

#2+5/y=12/(y^2)#

#2y^2+5y=12#

#2y^2+5y-12=0#

#y=(-5+-sqrt(5^2-4(2)(-12)))/(2(2))#

#=(-5+-sqrt(25+96))/4#

#=(-5+-sqrt(121))/4#

#=(-5+-11)/4#

#y=-4,3/2#

You may be excited to get an answer and stop, but remember that we used substitution, so substitute back:

#r=-3,5/2#

This does not conflict with the NPV, so the answer is good.

If you expand, you would have got:

#2r^2+r-15=0#

Then you would use the quadratic and the answer would be the same.