2/3n-1/6n=75

Solution for 2/3n-1/6n=75 equation:

2/3n-1/6n=75

We move all terms to the left:

2/3n-1/6n-(75)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We calculate fractions


12n/18n^2+(-3n)/18n^2-75=0

We multiply all the terms by the denominator


12n+(-3n)-75*18n^2=0

Wy multiply elements

-1350n^2+12n+(-3n)=0

We get rid of parentheses

-1350n^2+12n-3n=0

We add all the numbers together, and all the variables

-1350n^2+9n=0

a = -1350; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1350)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-1350}=\frac{-18}{-2700}
=1/150
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1350}=\frac{0}{-2700}
=0
$