z-(8/z)+2=0

Solution for z-(8/z)+2=0 equation:

z-(8/z)+2=0


Domain of the equation: z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

z-(+8/z)+2=0

We get rid of parentheses

z-8/z+2=0

We multiply all the terms by the denominator


z*z+2*z-8=0

We add all the numbers together, and all the variables

2z+z*z-8=0

Wy multiply elements

z^2+2z-8=0

a = 1; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*1}=\frac{-8}{2}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*1}=\frac{4}{2}
=2
$