8n+3=15/n

Solution for 8n+3=15/n equation:

8n+3=15/n

We move all terms to the left:

8n+3-(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)+3=0

We get rid of parentheses

8n-15/n+3=0

We multiply all the terms by the denominator


8n*n+3*n-15=0

We add all the numbers together, and all the variables

3n+8n*n-15=0

Wy multiply elements

8n^2+3n-15=0

a = 8; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·8·(-15)
Δ = 489
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{-(3)-\sqrt{489}}{2*8}=\frac{-3-\sqrt{489}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{489}}{2*8}=\frac{-3+\sqrt{489}}{16}
$