1/2x=22-x

Solution for 1/2x=22-x equation:

1/2x=22-x

We move all terms to the left:

1/2x-(22-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-(-1x+22)=0

We get rid of parentheses

1/2x+1x-22=0

We multiply all the terms by the denominator


1x*2x-22*2x+1=0

Wy multiply elements

2x^2-44x+1=0

a = 2; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·2·1
Δ = 1928
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:

$\sqrt{\Delta}=\sqrt{1928}=\sqrt{4*482}=\sqrt{4}*\sqrt{482}=2\sqrt{482}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{482}}{2*2}=\frac{44-2\sqrt{482}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{482}}{2*2}=\frac{44+2\sqrt{482}}{4}
$