3n+7=16/n

Solution for 3n+7=16/n equation:

3n+7=16/n

We move all terms to the left:

3n+7-(16/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

3n-(+16/n)+7=0

We get rid of parentheses

3n-16/n+7=0

We multiply all the terms by the denominator


3n*n+7*n-16=0

We add all the numbers together, and all the variables

7n+3n*n-16=0

Wy multiply elements

3n^2+7n-16=0

a = 3; b = 7; c = -16;
Δ = b2-4ac
Δ = 72-4·3·(-16)
Δ = 241
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{-(7)-\sqrt{241}}{2*3}=\frac{-7-\sqrt{241}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{241}}{2*3}=\frac{-7+\sqrt{241}}{6}
$