1/6n+10=2/3n

Solution for 1/6n+10=2/3n equation:

1/6n+10=2/3n

We move all terms to the left:

1/6n+10-(2/3n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/6n-(+2/3n)+10=0

We get rid of parentheses

1/6n-2/3n+10=0

We calculate fractions


3n/18n^2+(-12n)/18n^2+10=0

We multiply all the terms by the denominator


3n+(-12n)+10*18n^2=0

Wy multiply elements

180n^2+3n+(-12n)=0

We get rid of parentheses

180n^2+3n-12n=0

We add all the numbers together, and all the variables

180n^2-9n=0

a = 180; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·180·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*180}=\frac{0}{360}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*180}=\frac{18}{360}
=1/20
$