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

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

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

We move all terms to the left:

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


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



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

n∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

(-1n)/6n^2+(-6n)/6n^2+16=0

We multiply all the terms by the denominator


(-1n)+(-6n)+16*6n^2=0

Wy multiply elements

96n^2+(-1n)+(-6n)=0

We get rid of parentheses

96n^2-1n-6n=0

We add all the numbers together, and all the variables

96n^2-7n=0

a = 96; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·96·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*96}=\frac{0}{192}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*96}=\frac{14}{192}
=7/96
$