1/6n+1/3n=-4

Solution for 1/6n+1/3n=-4 equation:

1/6n+1/3n=-4

We move all terms to the left:

1/6n+1/3n-(-4)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

1/6n+1/3n+4=0

We calculate fractions


3n/18n^2+6n/18n^2+4=0

We multiply all the terms by the denominator


3n+6n+4*18n^2=0

We add all the numbers together, and all the variables

9n+4*18n^2=0

Wy multiply elements

72n^2+9n=0

a = 72; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·72·0
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*72}=\frac{-18}{144}
=-1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*72}=\frac{0}{144}
=0
$