3/9n-10=2/5n

Solution for 3/9n-10=2/5n equation:

3/9n-10=2/5n

We move all terms to the left:

3/9n-10-(2/5n)=0


Domain of the equation: 9n!=0

n!=0/9

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

3/9n-(+2/5n)-10=0

We get rid of parentheses

3/9n-2/5n-10=0

We calculate fractions


15n/45n^2+(-18n)/45n^2-10=0

We multiply all the terms by the denominator


15n+(-18n)-10*45n^2=0

Wy multiply elements

-450n^2+15n+(-18n)=0

We get rid of parentheses

-450n^2+15n-18n=0

We add all the numbers together, and all the variables

-450n^2-3n=0

a = -450; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-450)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-450}=\frac{0}{-900}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-450}=\frac{6}{-900}
=-1/150
$