z^2=9/64

Solution for z^2=9/64 equation:

z^2=9/64

We move all terms to the left:

z^2-(9/64)=0

We add all the numbers together, and all the variables

z^2-(+9/64)=0

We get rid of parentheses

z^2-9/64=0

We multiply all the terms by the denominator


z^2*64-9=0

Wy multiply elements

64z^2-9=0

a = 64; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·64·(-9)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*64}=\frac{-48}{128}
=-3/8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*64}=\frac{48}{128}
=3/8
$