15-1/5n=1/6n-1

Solution for 15-1/5n=1/6n-1 equation:

15-1/5n=1/6n-1

We move all terms to the left:

15-1/5n-(1/6n-1)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



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

n∈R


We get rid of parentheses

-1/5n-1/6n+1+15=0

We calculate fractions


(-6n)/30n^2+(-5n)/30n^2+1+15=0

We add all the numbers together, and all the variables

(-6n)/30n^2+(-5n)/30n^2+16=0

We multiply all the terms by the denominator


(-6n)+(-5n)+16*30n^2=0

Wy multiply elements

480n^2+(-6n)+(-5n)=0

We get rid of parentheses

480n^2-6n-5n=0

We add all the numbers together, and all the variables

480n^2-11n=0

a = 480; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·480·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*480}=\frac{0}{960}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*480}=\frac{22}{960}
=11/480
$