x+1/2x+x+20=180

Solution for x+1/2x+x+20=180 equation:

x+1/2x+x+20=180

We move all terms to the left:

x+1/2x+x+20-(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

2x+1/2x-160=0

We multiply all the terms by the denominator


2x*2x-160*2x+1=0

Wy multiply elements

4x^2-320x+1=0

a = 4; b = -320; c = +1;
Δ = b2-4ac
Δ = -3202-4·4·1
Δ = 102384
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:

$\sqrt{\Delta}=\sqrt{102384}=\sqrt{1296*79}=\sqrt{1296}*\sqrt{79}=36\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-36\sqrt{79}}{2*4}=\frac{320-36\sqrt{79}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+36\sqrt{79}}{2*4}=\frac{320+36\sqrt{79}}{8}
$