5/6n-2/3n=-1-1(-4)

Solution for 5/6n-2/3n=-1-1(-4) equation:

5/6n-2/3n=-1-1(-4)

We move all terms to the left:

5/6n-2/3n-(-1-1(-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

5/6n-2/3n-3=0

We calculate fractions


15n/18n^2+(-12n)/18n^2-3=0

We multiply all the terms by the denominator


15n+(-12n)-3*18n^2=0

Wy multiply elements

-54n^2+15n+(-12n)=0

We get rid of parentheses

-54n^2+15n-12n=0

We add all the numbers together, and all the variables

-54n^2+3n=0

a = -54; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-54)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-54}=\frac{-6}{-108}
=1/18
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-54}=\frac{0}{-108}
=0
$