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

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

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

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

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

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

We get rid of parentheses

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

We calculate fractions


(-36n^2)/300n^2+225n/300n^2+(-200n)/300n^2=0

We multiply all the terms by the denominator


(-36n^2)+225n+(-200n)=0

We get rid of parentheses

-36n^2+225n-200n=0

We add all the numbers together, and all the variables

-36n^2+25n=0

a = -36; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-36)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-36}=\frac{-50}{-72}
=25/36
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-36}=\frac{0}{-72}
=0
$