5/3n-1=3/2n+4

Solution for 5/3n-1=3/2n+4 equation:

5/3n-1=3/2n+4

We move all terms to the left:

5/3n-1-(3/2n+4)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n+4)!=0

n∈R


We get rid of parentheses

5/3n-3/2n-4-1=0

We calculate fractions


10n/6n^2+(-9n)/6n^2-4-1=0

We add all the numbers together, and all the variables

10n/6n^2+(-9n)/6n^2-5=0

We multiply all the terms by the denominator


10n+(-9n)-5*6n^2=0

Wy multiply elements

-30n^2+10n+(-9n)=0

We get rid of parentheses

-30n^2+10n-9n=0

We add all the numbers together, and all the variables

-30n^2+n=0

a = -30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-30}=\frac{-2}{-60}
=1/30
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-30}=\frac{0}{-60}
=0
$