z^2=49/64

Solution for z^2=49/64 equation:

z^2=49/64

We move all terms to the left:

z^2-(49/64)=0

We add all the numbers together, and all the variables

z^2-(+49/64)=0

We get rid of parentheses

z^2-49/64=0

We multiply all the terms by the denominator


z^2*64-49=0

Wy multiply elements

64z^2-49=0

a = 64; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·64·(-49)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112}{2*64}=\frac{-112}{128}
=-7/8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112}{2*64}=\frac{112}{128}
=7/8
$