1/2z+2/z=1

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

1/2z+2/z=1

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: z!=0

z∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5z-1*2z^2=0

Wy multiply elements

-2z^2+5z=0

a = -2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2}=\frac{0}{-4}
=0
$