2/3*z=8

Solution for 2/3*z=8 equation:

2/3*z=8

We move all terms to the left:

2/3*z-(8)=0


Domain of the equation: 3*z!=0

z!=0/1

z!=0

z∈R


We multiply all the terms by the denominator


-8*3*z+2=0

Wy multiply elements

-24z*z+2=0

Wy multiply elements

-24z^2+2=0

a = -24; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-24)·2
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-24}=\frac{0-8\sqrt{3}}{-48}
=-\frac{8\sqrt{3}}{-48}
=-\frac{\sqrt{3}}{-6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-24}=\frac{0+8\sqrt{3}}{-48}
=\frac{8\sqrt{3}}{-48}
=\frac{\sqrt{3}}{-6}
$