x+20=1/2(x)

Solution for x+20=1/2(x) equation:

x+20=1/2(x)

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-1/2x+20=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+40x-1=0

a = 2; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·2·(-1)
Δ = 1608
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:

$\sqrt{\Delta}=\sqrt{1608}=\sqrt{4*402}=\sqrt{4}*\sqrt{402}=2\sqrt{402}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{402}}{2*2}=\frac{-40-2\sqrt{402}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{402}}{2*2}=\frac{-40+2\sqrt{402}}{4}
$