1/2n=n+4

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

1/2n=n+4

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

1/2n-n-4=0

We multiply all the terms by the denominator


-n*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}
$