4/3z-2=2z

Solution for 4/3z-2=2z equation:

4/3z-2=2z

We move all terms to the left:

4/3z-2-(2z)=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+4/3z-2=0

We multiply all the terms by the denominator


-2z*3z-2*3z+4=0

Wy multiply elements

-6z^2-6z+4=0

a = -6; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-6)·4
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*-6}=\frac{6-2\sqrt{33}}{-12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*-6}=\frac{6+2\sqrt{33}}{-12}
$