44/n=n+8

Solution for 44/n=n+8 equation:

44/n=n+8

We move all terms to the left:

44/n-(n+8)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

44/n-n-8=0

We multiply all the terms by the denominator


-n*n-8*n+44=0

We add all the numbers together, and all the variables

-8n-n*n+44=0

Wy multiply elements

-1n^2-8n+44=0

a = -1; b = -8; c = +44;
Δ = b2-4ac
Δ = -82-4·(-1)·44
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*-1}=\frac{8-4\sqrt{15}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*-1}=\frac{8+4\sqrt{15}}{-2}
$