1/2z+1/2z=z+1

Solution for 1/2z+1/2z=z+1 equation:

1/2z+1/2z=z+1

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We get rid of parentheses

1/2z+1/2z-z-1=0

We multiply all the terms by the denominator


-z*2z-1*2z+1+1=0

We add all the numbers together, and all the variables

-z*2z-1*2z+2=0

Wy multiply elements

-2z^2-2z+2=0

a = -2; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-2)·2
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*-2}=\frac{2-2\sqrt{5}}{-4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*-2}=\frac{2+2\sqrt{5}}{-4}
$