SOLUTION: Solve the formula for the indicated letter. S = (1/3nr^2h + 4nrh), for r

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Question 173622This question is from textbook Introductory Algebra
: Solve the formula for the indicated letter.
S = (1/3nr^2h + 4nrh), for r This question is from textbook Introductory Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the formula for the indicated letter.
S = (1/3nr^2h + 4nrh), for r
:
1%2F3nr^2h + 4nrh = S
Multiply equation by 3 to get rid of the denominator
nr^2h + 3(4nrh) = 3S
:
nr^2h + 12nrh = 3S
:
Factor out nh:
nh(r^2 + 12r) = 3S
:
r^2 + 12r = %283S%29%2F%28nh%29
:
r^2 + 12r - %283S%29%2F%28nh%29 = 0
A quadratic equation where: a=1; b=12; c=-%283S%29%2F%28nh%29
Use the quadratic formula (we only want the positive solution here:
r+=+%28-12+%2B+sqrt%28+12%5E2+-+4+%2A+1+%2A+%28-3S%29%2F%28nh%29%29%29%2F%282%2A1%29+
r+=+%28-12+%2B+sqrt%28144+%2B+%2812S%29%2F%28nh%29%29%29%2F%282%29+