7/3n=4/n+1

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

7/3n=4/n+1

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: n+1)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


7n/3n^2+(-12n)/3n^2-1=0

We multiply all the terms by the denominator


7n+(-12n)-1*3n^2=0

Wy multiply elements

-3n^2+7n+(-12n)=0

We get rid of parentheses

-3n^2+7n-12n=0

We add all the numbers together, and all the variables

-3n^2-5n=0

a = -3; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-3)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-3}=\frac{0}{-6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-3}=\frac{10}{-6}
=-1+2/3
$