3/z+8/2z=2

Solution for 3/z+8/2z=2 equation:

3/z+8/2z=2

We move all terms to the left:

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


Domain of the equation: z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We calculate fractions


6z/2z^2+8z/2z^2-2=0

We multiply all the terms by the denominator


6z+8z-2*2z^2=0

We add all the numbers together, and all the variables

14z-2*2z^2=0

Wy multiply elements

-4z^2+14z=0

a = -4; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-4)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-4}=\frac{-28}{-8}
=3+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-4}=\frac{0}{-8}
=0
$