(17/9)-1/2n=1/6n+1

Solution for (17/9)-1/2n=1/6n+1 equation:

(17/9)-1/2n=1/6n+1

We move all terms to the left:

(17/9)-1/2n-(1/6n+1)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 6n+1)!=0

n∈R


We add all the numbers together, and all the variables

-1/2n-(1/6n+1)+(+17/9)=0

We get rid of parentheses

-1/2n-1/6n-1+17/9=0

We calculate fractions


1224n^2/972n^2+(-486n)/972n^2+(-162n)/972n^2-1=0

We multiply all the terms by the denominator


1224n^2+(-486n)+(-162n)-1*972n^2=0

Wy multiply elements

1224n^2-972n^2+(-486n)+(-162n)=0

We get rid of parentheses

1224n^2-972n^2-486n-162n=0

We add all the numbers together, and all the variables

252n^2-648n=0

a = 252; b = -648; c = 0;
Δ = b2-4ac
Δ = -6482-4·252·0
Δ = 419904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{419904}=648$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-648}{2*252}=\frac{0}{504}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+648}{2*252}=\frac{1296}{504}
=2+4/7
$