x+20=1/2x+108

Solution for x+20=1/2x+108 equation:

x+20=1/2x+108

We move all terms to the left:

x+20-(1/2x+108)=0


Domain of the equation: 2x+108)!=0

x∈R


We get rid of parentheses

x-1/2x-108+20=0

We multiply all the terms by the denominator


x*2x-108*2x+20*2x-1=0

Wy multiply elements

2x^2-216x+40x-1=0

We add all the numbers together, and all the variables

2x^2-176x-1=0

a = 2; b = -176; c = -1;
Δ = b2-4ac
Δ = -1762-4·2·(-1)
Δ = 30984
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:

$\sqrt{\Delta}=\sqrt{30984}=\sqrt{4*7746}=\sqrt{4}*\sqrt{7746}=2\sqrt{7746}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-2\sqrt{7746}}{2*2}=\frac{176-2\sqrt{7746}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+2\sqrt{7746}}{2*2}=\frac{176+2\sqrt{7746}}{4}
$