1/3n-1n=3

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

1/3n-1n=3

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/3n-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3n^2-9n+1=0

a = -3; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-3)·1
Δ = 93
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{-(-9)-\sqrt{93}}{2*-3}=\frac{9-\sqrt{93}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{93}}{2*-3}=\frac{9+\sqrt{93}}{-6}
$