k^2-16k+64=9k^2

Solution for k^2-16k+64=9k^2 equation:

k^2-16k+64=9k^2

We move all terms to the left:

k^2-16k+64-(9k^2)=0

determiningTheFunctionDomain
k^2-9k^2-16k+64=0

We add all the numbers together, and all the variables

-8k^2-16k+64=0

a = -8; b = -16; c = +64;
Δ = b2-4ac
Δ = -162-4·(-8)·64
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-48}{2*-8}=\frac{-32}{-16}
=+2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+48}{2*-8}=\frac{64}{-16}
=-4
$