6n+6/2n+11=180

Solution for 6n+6/2n+11=180 equation:

6n+6/2n+11=180

We move all terms to the left:

6n+6/2n+11-(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

6n+6/2n-169=0

We multiply all the terms by the denominator


6n*2n-169*2n+6=0

Wy multiply elements

12n^2-338n+6=0

a = 12; b = -338; c = +6;
Δ = b2-4ac
Δ = -3382-4·12·6
Δ = 113956
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:

$\sqrt{\Delta}=\sqrt{113956}=\sqrt{4*28489}=\sqrt{4}*\sqrt{28489}=2\sqrt{28489}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-338)-2\sqrt{28489}}{2*12}=\frac{338-2\sqrt{28489}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-338)+2\sqrt{28489}}{2*12}=\frac{338+2\sqrt{28489}}{24}
$