n/2n=n+3

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

n/2n=n+3

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

n/2n-n-3=0

We multiply all the terms by the denominator


n-n*2n-3*2n=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-2n^2-5n=0

a = -2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-2}=\frac{0}{-4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-2}=\frac{10}{-4}
=-2+1/2
$