3/2k^2-16=80

Solution for 3/2k^2-16=80 equation:

3/2k^2-16=80

We move all terms to the left:

3/2k^2-16-(80)=0


Domain of the equation: 2k^2!=0

k^2!=0/2

k^2!=√0

k!=0

k∈R


We add all the numbers together, and all the variables

3/2k^2-96=0

We multiply all the terms by the denominator


-96*2k^2+3=0

Wy multiply elements

-192k^2+3=0

a = -192; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-192)·3
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{-(0)-48}{2*-192}=\frac{-48}{-384}
=1/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*-192}=\frac{48}{-384}
=-1/8
$