1/7n-4=1/3n

Solution for 1/7n-4=1/3n equation:

1/7n-4=1/3n

We move all terms to the left:

1/7n-4-(1/3n)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/7n-(+1/3n)-4=0

We get rid of parentheses

1/7n-1/3n-4=0

We calculate fractions


3n/21n^2+(-7n)/21n^2-4=0

We multiply all the terms by the denominator


3n+(-7n)-4*21n^2=0

Wy multiply elements

-84n^2+3n+(-7n)=0

We get rid of parentheses

-84n^2+3n-7n=0

We add all the numbers together, and all the variables

-84n^2-4n=0

a = -84; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-84)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-84}=\frac{0}{-168}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-84}=\frac{8}{-168}
=-1/21
$