-8/3n+21=-1/2n

Solution for -8/3n+21=-1/2n equation:

-8/3n+21=-1/2n

We move all terms to the left:

-8/3n+21-(-1/2n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

-8/3n+1/2n+21=0

We calculate fractions


(-16n)/6n^2+3n/6n^2+21=0

We multiply all the terms by the denominator


(-16n)+3n+21*6n^2=0

We add all the numbers together, and all the variables

3n+(-16n)+21*6n^2=0

Wy multiply elements

126n^2+3n+(-16n)=0

We get rid of parentheses

126n^2+3n-16n=0

We add all the numbers together, and all the variables

126n^2-13n=0

a = 126; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·126·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*126}=\frac{0}{252}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*126}=\frac{26}{252}
=13/126
$