1/2(2n)=n

Solution for 1/2(2n)=n equation:

1/2(2n)=n

We move all terms to the left:

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


Domain of the equation: 22n!=0

n!=0/22

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/22n=0

We multiply all the terms by the denominator


-1n*22n+1=0

Wy multiply elements

-22n^2+1=0

a = -22; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-22)·1
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{22}}{2*-22}=\frac{0-2\sqrt{22}}{-44}
=-\frac{2\sqrt{22}}{-44}
=-\frac{\sqrt{22}}{-22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{22}}{2*-22}=\frac{0+2\sqrt{22}}{-44}
=\frac{2\sqrt{22}}{-44}
=\frac{\sqrt{22}}{-22}
$