2z+2z/z=10

Solution for 2z+2z/z=10 equation:

2z+2z/z=10

We move all terms to the left:

2z+2z/z-(10)=0


Domain of the equation: z!=0

z∈R


We multiply all the terms by the denominator


2z*z+2z-10*z=0

We add all the numbers together, and all the variables

-8z+2z*z=0

Wy multiply elements

2z^2-8z=0

a = 2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·2·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*2}=\frac{0}{4}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*2}=\frac{16}{4}
=4
$