n=3/12n-1

Solution for n=3/12n-1 equation:

n=3/12n-1

We move all terms to the left:

n-(3/12n-1)=0


Domain of the equation: 12n-1)!=0

n∈R


We get rid of parentheses

n-3/12n+1=0

We multiply all the terms by the denominator


n*12n+1*12n-3=0

Wy multiply elements

12n^2+12n-3=0

a = 12; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·12·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*12}=\frac{-12-12\sqrt{2}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*12}=\frac{-12+12\sqrt{2}}{24}
$