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 = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-18\sqrt{6}}{2*2}=\frac{44-18\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+18\sqrt{6}}{2*2}=\frac{44+18\sqrt{6}}{4}
$