1/2x-1/2x=x+1

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

1/2x-1/2x=x+1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-1/2x-x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-x*2x-1*2x=0

Wy multiply elements

-2x^2-2x=0

a = -2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-2}=\frac{4}{-4}
=-1
$