-4/15n+2/3=2/5n

Solution for -4/15n+2/3=2/5n equation:

-4/15n+2/3=2/5n

We move all terms to the left:

-4/15n+2/3-(2/5n)=0


Domain of the equation: 15n!=0

n!=0/15

n!=0

n∈R



Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-4/15n-(+2/5n)+2/3=0

We get rid of parentheses

-4/15n-2/5n+2/3=0

We calculate fractions


750n^2/675n^2+(-180n)/675n^2+(-270n)/675n^2=0

We multiply all the terms by the denominator


750n^2+(-180n)+(-270n)=0

We get rid of parentheses

750n^2-180n-270n=0

We add all the numbers together, and all the variables

750n^2-450n=0

a = 750; b = -450; c = 0;
Δ = b2-4ac
Δ = -4502-4·750·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-450}{2*750}=\frac{0}{1500}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+450}{2*750}=\frac{900}{1500}
=3/5
$