n2+3n+12n2+18n=180

Solution for n2+3n+12n2+18n=180 equation:

n2+3n+12n^2+18n=180

We move all terms to the left:

n2+3n+12n^2+18n-(180)=0

We add all the numbers together, and all the variables

13n^2+21n-180=0

a = 13; b = 21; c = -180;
Δ = b2-4ac
Δ = 212-4·13·(-180)
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-99}{2*13}=\frac{-120}{26}
=-4+8/13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+99}{2*13}=\frac{78}{26}
=3
$