1/2x=20+x

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

1/2x=20+x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2x-x-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}
$