X=22-1/2x

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

X=22-1/2X

We move all terms to the left:

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

We get rid of parentheses

X+1/2X-22=0

We multiply all the terms by the denominator


X*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}
$