2n+6=5*3/n

Solution for 2n+6=5*3/n equation:

2n+6=5*3/n

We move all terms to the left:

2n+6-(5*3/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

2n-(+5*3/n)+6=0

We get rid of parentheses

2n-5*3/n+6=0

We multiply all the terms by the denominator


2n*n+6*n-5*3=0

We add all the numbers together, and all the variables

6n+2n*n-15=0

Wy multiply elements

2n^2+6n-15=0

a = 2; b = 6; c = -15;
Δ = b2-4ac
Δ = 62-4·2·(-15)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*2}=\frac{-6-2\sqrt{39}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*2}=\frac{-6+2\sqrt{39}}{4}
$