55n=5/6n

Solution for 55n=5/6n equation:

55n=5/6n

We move all terms to the left:

55n-(5/6n)=0


Domain of the equation: 6n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

55n-(+5/6n)=0

We get rid of parentheses

55n-5/6n=0

We multiply all the terms by the denominator


55n*6n-5=0

Wy multiply elements

330n^2-5=0

a = 330; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·330·(-5)
Δ = 6600
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:

$\sqrt{\Delta}=\sqrt{6600}=\sqrt{100*66}=\sqrt{100}*\sqrt{66}=10\sqrt{66}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{66}}{2*330}=\frac{0-10\sqrt{66}}{660}
=-\frac{10\sqrt{66}}{660}
=-\frac{\sqrt{66}}{66}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{66}}{2*330}=\frac{0+10\sqrt{66}}{660}
=\frac{10\sqrt{66}}{660}
=\frac{\sqrt{66}}{66}
$