3n-5/n=-1

Solution for 3n-5/n=-1 equation:

3n-5/n=-1

We move all terms to the left:

3n-5/n-(-1)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

3n-5/n+1=0

We multiply all the terms by the denominator


3n*n+1*n-5=0

We add all the numbers together, and all the variables

n+3n*n-5=0

Wy multiply elements

3n^2+n-5=0

a = 3; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·3·(-5)
Δ = 61
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{-(1)-\sqrt{61}}{2*3}=\frac{-1-\sqrt{61}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*3}=\frac{-1+\sqrt{61}}{6}
$