1/2z+1-z=-1

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

1/2z+1-z=-1

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2z^2+4z+1=0

a = -2; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-2)·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*-2}=\frac{-4-2\sqrt{6}}{-4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*-2}=\frac{-4+2\sqrt{6}}{-4}
$