-2/3n-2/5n=-22/15

Solution for -2/3n-2/5n=-22/15 equation:

-2/3n-2/5n=-22/15

We move all terms to the left:

-2/3n-2/5n-(-22/15)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

-2/3n-2/5n+22/15=0

We calculate fractions


1650n^2/225n^2+(-150n)/225n^2+(-90n)/225n^2=0

We multiply all the terms by the denominator


1650n^2+(-150n)+(-90n)=0

We get rid of parentheses

1650n^2-150n-90n=0

We add all the numbers together, and all the variables

1650n^2-240n=0

a = 1650; b = -240; c = 0;
Δ = b2-4ac
Δ = -2402-4·1650·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-240}{2*1650}=\frac{0}{3300}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+240}{2*1650}=\frac{480}{3300}
=8/55
$