12/n=24n=

Solution for 12/n=24n= equation:

12/n=24n=

We move all terms to the left:

12/n-(24n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-24n+12/n=0

We multiply all the terms by the denominator


-24n*n+12=0

Wy multiply elements

-24n^2+12=0

a = -24; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-24)·12
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-24}=\frac{0-24\sqrt{2}}{-48}
=-\frac{24\sqrt{2}}{-48}
=-\frac{\sqrt{2}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-24}=\frac{0+24\sqrt{2}}{-48}
=\frac{24\sqrt{2}}{-48}
=\frac{\sqrt{2}}{-2}
$