SOLUTION: Given that p=re^2/(r+b)^2 make r the subject formula

Clear the fraction by multiplying both sides by 



Square out  as 



Remove the parentheses by distributing:



Get the term with  first, then terms with r then other terms:



Factor r out of the two terms that contain r:



Use the quadratic formula: 
with x=r, A=p, B=(2pb-e2) and C=pb^2 



remove the parentheses of the first term in the numerator
Square the binomial under the square root radical:



The  and  cancel under the square root radical:



Factor out  under the square root radical



Take out the the square root of  as e in front of the square root



Reverse the terms under the radical so the positive term comes first
which makes the + sign unnecessary:



Edwin