z^2=16/81

Solution for z^2=16/81 equation:

z^2=16/81

We move all terms to the left:

z^2-(16/81)=0

We add all the numbers together, and all the variables

z^2-(+16/81)=0

We get rid of parentheses

z^2-16/81=0

We multiply all the terms by the denominator


z^2*81-16=0

Wy multiply elements

81z^2-16=0

a = 81; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·81·(-16)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*81}=\frac{-72}{162}
=-4/9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*81}=\frac{72}{162}
=4/9
$