1/2n+5=n

Solution for 1/2n+5=n equation:

1/2n+5=n

We move all terms to the left:

1/2n+5-(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+5=0

We multiply all the terms by the denominator


-1n*2n+5*2n+1=0

Wy multiply elements

-2n^2+10n+1=0

a = -2; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-2)·1
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{3}}{2*-2}=\frac{-10-6\sqrt{3}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{3}}{2*-2}=\frac{-10+6\sqrt{3}}{-4}
$