15-1/9n=1/6n-1

Solution for 15-1/9n=1/6n-1 equation:

15-1/9n=1/6n-1

We move all terms to the left:

15-1/9n-(1/6n-1)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



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

n∈R


We get rid of parentheses

-1/9n-1/6n+1+15=0

We calculate fractions


(-6n)/54n^2+(-9n)/54n^2+1+15=0

We add all the numbers together, and all the variables

(-6n)/54n^2+(-9n)/54n^2+16=0

We multiply all the terms by the denominator


(-6n)+(-9n)+16*54n^2=0

Wy multiply elements

864n^2+(-6n)+(-9n)=0

We get rid of parentheses

864n^2-6n-9n=0

We add all the numbers together, and all the variables

864n^2-15n=0

a = 864; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·864·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*864}=\frac{0}{1728}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*864}=\frac{30}{1728}
=5/288
$