8n-20=15/n

Solution for 8n-20=15/n equation:

8n-20=15/n

We move all terms to the left:

8n-20-(15/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

8n-(+15/n)-20=0

We get rid of parentheses

8n-15/n-20=0

We multiply all the terms by the denominator


8n*n-20*n-15=0

We add all the numbers together, and all the variables

-20n+8n*n-15=0

Wy multiply elements

8n^2-20n-15=0

a = 8; b = -20; c = -15;
Δ = b2-4ac
Δ = -202-4·8·(-15)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{55}}{2*8}=\frac{20-4\sqrt{55}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{55}}{2*8}=\frac{20+4\sqrt{55}}{16}
$