12/n=n

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Solution for 12/n=n equation:



12/n=n
We move all terms to the left:
12/n-(n)=0
Domain of the equation: n!=0
n∈R
We add all the numbers together, and all the variables
-1n+12/n=0
We multiply all the terms by the denominator
-1n*n+12=0
Wy multiply elements
-1n^2+12=0
a = -1; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-1)·12
Δ = 48
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:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-1}=\frac{0-4\sqrt{3}}{-2} =-\frac{4\sqrt{3}}{-2} =-\frac{2\sqrt{3}}{-1} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-1}=\frac{0+4\sqrt{3}}{-2} =\frac{4\sqrt{3}}{-2} =\frac{2\sqrt{3}}{-1} $

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