X=1+1/2*x

Solution for X=1+1/2*x equation:

X=1+1/2X

We move all terms to the left:

X-(1+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+1)=0

We get rid of parentheses

X-1/2X-1=0

We multiply all the terms by the denominator


X*2X-1*2X-1=0

Wy multiply elements

2X^2-2X-1=0

a = 2; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·2·(-1)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*2}=\frac{2-2\sqrt{3}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*2}=\frac{2+2\sqrt{3}}{4}
$