k^2=25/64

Solution for k^2=25/64 equation:

k^2=25/64

We move all terms to the left:

k^2-(25/64)=0

We add all the numbers together, and all the variables

k^2-(+25/64)=0

We get rid of parentheses

k^2-25/64=0

We multiply all the terms by the denominator


k^2*64-25=0

Wy multiply elements

64k^2-25=0

a = 64; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·64·(-25)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*64}=\frac{-80}{128}
=-5/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*64}=\frac{80}{128}
=5/8
$