How do you solve for n in (9n+4)+(3n^2 - 0.75) = 180?

1 Answer
Jul 7, 2018

n_1=sqrt(2202)/6-9/6 or n_2=-9/6-sqrt(2202)/6

Explanation:

Simplifying your equation

3n^2+9n+4-3/4-180=0

we have

4-3/4-180=(16-3-360)/4=-707/4

so we have to solve

3n^2+9n-707/4=0
dividing by 3 we get

n^2+3n-707/12=0

by the quadratic formula we get

n_(1,2)=-3/2\pm sqrt(367/6)

this is

n_(1,2)=-3/2pm sqrt(2202)/6

so we get

n_1=(sqrt(2202)-9)/6

n_2=-1/6(9+sqrt(2202))