Z(81z^2-1)=0

Solution for Z(81z^2-1)=0 equation:

(81Z^2-1)=0

We get rid of parentheses

81Z^2-1=0

a = 81; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·81·(-1)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*81}=\frac{-18}{162}
=-1/9
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*81}=\frac{18}{162}
=1/9
$