1/2n+4=n

Solution for 1/2n+4=n equation:

1/2n+4=n

We move all terms to the left:

1/2n+4-(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+4=0

We multiply all the terms by the denominator


-1n*2n+4*2n+1=0

Wy multiply elements

-2n^2+8n+1=0

a = -2; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-2)·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{2}}{2*-2}=\frac{-8-6\sqrt{2}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{2}}{2*-2}=\frac{-8+6\sqrt{2}}{-4}
$