3n=2/n-5

Solution for 3n=2/n-5 equation:

3n=2/n-5

We move all terms to the left:

3n-(2/n-5)=0


Domain of the equation: n-5)!=0

n∈R


We get rid of parentheses

3n-2/n+5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5n+3n*n-2=0

Wy multiply elements

3n^2+5n-2=0

a = 3; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·3·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*3}=\frac{-12}{6}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*3}=\frac{2}{6}
=1/3
$