2/3z-z=z

Solution for 2/3z-z=z equation:

2/3z-z=z

We move all terms to the left:

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


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We add all the numbers together, and all the variables

-2z+2/3z=0

We multiply all the terms by the denominator


-2z*3z+2=0

Wy multiply elements

-6z^2+2=0

a = -6; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-6)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-6}=\frac{0-4\sqrt{3}}{-12}
=-\frac{4\sqrt{3}}{-12}
=-\frac{\sqrt{3}}{-3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-6}=\frac{0+4\sqrt{3}}{-12}
=\frac{4\sqrt{3}}{-12}
=\frac{\sqrt{3}}{-3}
$