3/n=n+1

Solution for 3/n=n+1 equation:

3/n=n+1

We move all terms to the left:

3/n-(n+1)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

3/n-n-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1n-n*n+3=0

Wy multiply elements

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

a = -1; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-1)·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{13}}{2*-1}=\frac{1-\sqrt{13}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*-1}=\frac{1+\sqrt{13}}{-2}
$