x+1/2x+2-2x=180

Solution for x+1/2x+2-2x=180 equation:

x+1/2x+2-2x=180

We move all terms to the left:

x+1/2x+2-2x-(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

-1x+1/2x-178=0

We multiply all the terms by the denominator


-1x*2x-178*2x+1=0

Wy multiply elements

-2x^2-356x+1=0

a = -2; b = -356; c = +1;
Δ = b2-4ac
Δ = -3562-4·(-2)·1
Δ = 126744
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:

$\sqrt{\Delta}=\sqrt{126744}=\sqrt{4*31686}=\sqrt{4}*\sqrt{31686}=2\sqrt{31686}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-356)-2\sqrt{31686}}{2*-2}=\frac{356-2\sqrt{31686}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-356)+2\sqrt{31686}}{2*-2}=\frac{356+2\sqrt{31686}}{-4}
$