2c+6+1/2c+5=180

Solution for 2c+6+1/2c+5=180 equation:

2c+6+1/2c+5=180

We move all terms to the left:

2c+6+1/2c+5-(180)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

2c+1/2c-169=0

We multiply all the terms by the denominator


2c*2c-169*2c+1=0

Wy multiply elements

4c^2-338c+1=0

a = 4; b = -338; c = +1;
Δ = b2-4ac
Δ = -3382-4·4·1
Δ = 114228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{114228}=\sqrt{36*3173}=\sqrt{36}*\sqrt{3173}=6\sqrt{3173}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-338)-6\sqrt{3173}}{2*4}=\frac{338-6\sqrt{3173}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-338)+6\sqrt{3173}}{2*4}=\frac{338+6\sqrt{3173}}{8}
$