0=16k^2-9

Solution for 0=16k^2-9 equation:

0=16k^2-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(16k^2-9)=0

We get rid of parentheses

-16k^2+9=0

a = -16; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-16)·9
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-16}=\frac{-24}{-32}
=3/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-16}=\frac{24}{-32}
=-3/4
$