3*4^2k/8=24

Solution for 3*4^2k/8=24 equation:

3*4^2k/8=24

We move all terms to the left:

3*4^2k/8-(24)=0

We multiply all the terms by the denominator


3*4^2k-24*8=0

We add all the numbers together, and all the variables

3*4^2k-192=0

Wy multiply elements

12k^2-192=0

a = 12; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·12·(-192)
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*12}=\frac{-96}{24}
=-4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*12}=\frac{96}{24}
=4
$