96/k=3k

Solution for 96/k=3k equation:

96/k=3k

We move all terms to the left:

96/k-(3k)=0


Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

-3k+96/k=0

We multiply all the terms by the denominator


-3k*k+96=0

Wy multiply elements

-3k^2+96=0

a = -3; b = 0; c = +96;
Δ = b2-4ac
Δ = 02-4·(-3)·96
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-3}=\frac{0-24\sqrt{2}}{-6}
=-\frac{24\sqrt{2}}{-6}
=-\frac{4\sqrt{2}}{-1}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-3}=\frac{0+24\sqrt{2}}{-6}
=\frac{24\sqrt{2}}{-6}
=\frac{4\sqrt{2}}{-1}
$