1/3n-7=5/3n+-5n=

Solution for 1/3n-7=5/3n+-5n= equation:

1/3n-7=5/3n+-5n=

We move all terms to the left:

1/3n-7-(5/3n+-5n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 3n+-5n)!=0

n∈R


We add all the numbers together, and all the variables

1/3n-(-5n+5/3n)-7=0

We get rid of parentheses

1/3n+5n-5/3n-7=0

We multiply all the terms by the denominator


5n*3n-7*3n+1-5=0

We add all the numbers together, and all the variables

5n*3n-7*3n-4=0

Wy multiply elements

15n^2-21n-4=0

a = 15; b = -21; c = -4;
Δ = b2-4ac
Δ = -212-4·15·(-4)
Δ = 681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{681}}{2*15}=\frac{21-\sqrt{681}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{681}}{2*15}=\frac{21+\sqrt{681}}{30}
$