112/2^n=n

Solution for 112/2^n=n equation:

112/2^n=n

We move all terms to the left:

112/2^n-(n)=0


Domain of the equation: 2^n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+112/2^n=0

We multiply all the terms by the denominator


-1n*2^n+112=0

Wy multiply elements

-2n^2+112=0

a = -2; b = 0; c = +112;
Δ = b2-4ac
Δ = 02-4·(-2)·112
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*-2}=\frac{0-8\sqrt{14}}{-4}
=-\frac{8\sqrt{14}}{-4}
=-\frac{2\sqrt{14}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*-2}=\frac{0+8\sqrt{14}}{-4}
=\frac{8\sqrt{14}}{-4}
=\frac{2\sqrt{14}}{-1}
$