1/2n+1/2n+n=180

Solution for 1/2n+1/2n+n=180 equation:

1/2n+1/2n+n=180

We move all terms to the left:

1/2n+1/2n+n-(180)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

n+1/2n+1/2n-180=0

We multiply all the terms by the denominator


n*2n-180*2n+1+1=0

We add all the numbers together, and all the variables

n*2n-180*2n+2=0

Wy multiply elements

2n^2-360n+2=0

a = 2; b = -360; c = +2;
Δ = b2-4ac
Δ = -3602-4·2·2
Δ = 129584
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:

$\sqrt{\Delta}=\sqrt{129584}=\sqrt{16*8099}=\sqrt{16}*\sqrt{8099}=4\sqrt{8099}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8099}}{2*2}=\frac{360-4\sqrt{8099}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8099}}{2*2}=\frac{360+4\sqrt{8099}}{4}
$