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

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

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

We move all terms to the left:

180-(2c+6+3c+4+1/2c+5)=0


Domain of the equation: 2c+5)!=0

c∈R


We add all the numbers together, and all the variables

-(5c+1/2c+15)+180=0

We get rid of parentheses

-5c-1/2c-15+180=0

We multiply all the terms by the denominator


-5c*2c-15*2c+180*2c-1=0

Wy multiply elements

-10c^2-30c+360c-1=0

We add all the numbers together, and all the variables

-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}
$