X-12+2x-220+1/2x+6=180

Solution for X-12+2x-220+1/2x+6=180 equation:

X-12+2X-220+1/2X+6=180

We move all terms to the left:

X-12+2X-220+1/2X+6-(180)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/2X-406=0

We multiply all the terms by the denominator


3X*2X-406*2X+1=0

Wy multiply elements

6X^2-812X+1=0

a = 6; b = -812; c = +1;
Δ = b2-4ac
Δ = -8122-4·6·1
Δ = 659320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{659320}=\sqrt{4*164830}=\sqrt{4}*\sqrt{164830}=2\sqrt{164830}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-812)-2\sqrt{164830}}{2*6}=\frac{812-2\sqrt{164830}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-812)+2\sqrt{164830}}{2*6}=\frac{812+2\sqrt{164830}}{12}
$