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

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

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

We move all terms to the left:

1/2x+2+x+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

3x+1/2x-178=0

We multiply all the terms by the denominator


3x*2x-178*2x+1=0

Wy multiply elements

6x^2-356x+1=0

a = 6; b = -356; c = +1;
Δ = b2-4ac
Δ = -3562-4·6·1
Δ = 126712
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:

$\sqrt{\Delta}=\sqrt{126712}=\sqrt{4*31678}=\sqrt{4}*\sqrt{31678}=2\sqrt{31678}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-356)-2\sqrt{31678}}{2*6}=\frac{356-2\sqrt{31678}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-356)+2\sqrt{31678}}{2*6}=\frac{356+2\sqrt{31678}}{12}
$