X+1/2x+20=180

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

X+1/2X+20=180

We move all terms to the left:

X+1/2X+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

X+1/2X-160=0

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2-320X+1=0

a = 2; b = -320; c = +1;
Δ = b2-4ac
Δ = -3202-4·2·1
Δ = 102392
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:

$\sqrt{\Delta}=\sqrt{102392}=\sqrt{4*25598}=\sqrt{4}*\sqrt{25598}=2\sqrt{25598}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-2\sqrt{25598}}{2*2}=\frac{320-2\sqrt{25598}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+2\sqrt{25598}}{2*2}=\frac{320+2\sqrt{25598}}{4}
$