(2n+4)3n=180

Solution for (2n+4)3n=180 equation:

(2n+4)3n=180

We move all terms to the left:

(2n+4)3n-(180)=0

We multiply parentheses

6n^2+12n-180=0

a = 6; b = 12; c = -180;
Δ = b2-4ac
Δ = 122-4·6·(-180)
Δ = 4464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{31}}{2*6}=\frac{-12-12\sqrt{31}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{31}}{2*6}=\frac{-12+12\sqrt{31}}{12}
$