1/2n-2/3n=-1/15

Solution for 1/2n-2/3n=-1/15 equation:

1/2n-2/3n=-1/15

We move all terms to the left:

1/2n-2/3n-(-1/15)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

1/2n-2/3n+1/15=0

We calculate fractions


18n^2/90n^2+45n/90n^2+(-60n)/90n^2=0

We multiply all the terms by the denominator


18n^2+45n+(-60n)=0

We get rid of parentheses

18n^2+45n-60n=0

We add all the numbers together, and all the variables

18n^2-15n=0

a = 18; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·18·0
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*18}=\frac{0}{36}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*18}=\frac{30}{36}
=5/6
$