64k^2+1=5

Solution for 64k^2+1=5 equation:

64k^2+1=5

We move all terms to the left:

64k^2+1-(5)=0

We add all the numbers together, and all the variables

64k^2-4=0

a = 64; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·64·(-4)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*64}=\frac{-32}{128}
=-1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*64}=\frac{32}{128}
=1/4
$