64k^2+6=42

Solution for 64k^2+6=42 equation:

64k^2+6=42

We move all terms to the left:

64k^2+6-(42)=0

We add all the numbers together, and all the variables

64k^2-36=0

a = 64; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·64·(-36)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*64}=\frac{-96}{128}
=-3/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*64}=\frac{96}{128}
=3/4
$