4/n+5=5/3n+1

Solution for 4/n+5=5/3n+1 equation:

4/n+5=5/3n+1

We move all terms to the left:

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


Domain of the equation: n!=0

n∈R



Domain of the equation: 3n+1)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


12n/3n^2+(-5n)/3n^2-1+5=0

We add all the numbers together, and all the variables

12n/3n^2+(-5n)/3n^2+4=0

We multiply all the terms by the denominator


12n+(-5n)+4*3n^2=0

Wy multiply elements

12n^2+12n+(-5n)=0

We get rid of parentheses

12n^2+12n-5n=0

We add all the numbers together, and all the variables

12n^2+7n=0

a = 12; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·12·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*12}=\frac{-14}{24}
=-7/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*12}=\frac{0}{24}
=0
$