12+1/2n=n

Solution for 12+1/2n=n equation:

12+1/2n=n

We move all terms to the left:

12+1/2n-(n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/2n+12=0

We multiply all the terms by the denominator


-1n*2n+12*2n+1=0

Wy multiply elements

-2n^2+24n+1=0

a = -2; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-2)·1
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{146}}{2*-2}=\frac{-24-2\sqrt{146}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{146}}{2*-2}=\frac{-24+2\sqrt{146}}{-4}
$