15/n=2+n

Solution for 15/n=2+n equation:

15/n=2+n

We move all terms to the left:

15/n-(2+n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

15/n-(n+2)=0

We get rid of parentheses

15/n-n-2=0

We multiply all the terms by the denominator


-n*n-2*n+15=0

We add all the numbers together, and all the variables

-2n-n*n+15=0

Wy multiply elements

-1n^2-2n+15=0

a = -1; b = -2; c = +15;
Δ = b2-4ac
Δ = -22-4·(-1)·15
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-1}=\frac{-6}{-2}
=+3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-1}=\frac{10}{-2}
=-5
$