3c+4+2c+6+1/2c+5=180

Solution for 3c+4+2c+6+1/2c+5=180 equation:

3c+4+2c+6+1/2c+5=180

We move all terms to the left:

3c+4+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

5c+1/2c-165=0

We multiply all the terms by the denominator


5c*2c-165*2c+1=0

Wy multiply elements

10c^2-330c+1=0

a = 10; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·10·1
Δ = 108860
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:

$\sqrt{\Delta}=\sqrt{108860}=\sqrt{4*27215}=\sqrt{4}*\sqrt{27215}=2\sqrt{27215}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27215}}{2*10}=\frac{330-2\sqrt{27215}}{20}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27215}}{2*10}=\frac{330+2\sqrt{27215}}{20}
$