(9z/108)6z=8

Solution for (9z/108)6z=8 equation:

(9z/108)6z=8

We move all terms to the left:

(9z/108)6z-(8)=0


Domain of the equation: 108)6z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

(+9z/108)6z-8=0

We multiply parentheses

54z^2-8=0

a = 54; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·54·(-8)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*54}=\frac{0-24\sqrt{3}}{108}
=-\frac{24\sqrt{3}}{108}
=-\frac{2\sqrt{3}}{9}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*54}=\frac{0+24\sqrt{3}}{108}
=\frac{24\sqrt{3}}{108}
=\frac{2\sqrt{3}}{9}
$