144/n=n

Solution for 144/n=n equation:

144/n=n

We move all terms to the left:

144/n-(n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-1n+144/n=0

We multiply all the terms by the denominator


-1n*n+144=0

Wy multiply elements

-1n^2+144=0

a = -1; b = 0; c = +144;
Δ = b2-4ac
Δ = 02-4·(-1)·144
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-1}=\frac{-24}{-2}
=+12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-1}=\frac{24}{-2}
=-12
$