1/2n+3=n

Solution for 1/2n+3=n equation:

1/2n+3=n

We move all terms to the left:

1/2n+3-(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+3=0

We multiply all the terms by the denominator


-1n*2n+3*2n+1=0

Wy multiply elements

-2n^2+6n+1=0

a = -2; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-2)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*-2}=\frac{-6-2\sqrt{11}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*-2}=\frac{-6+2\sqrt{11}}{-4}
$