3/5n+15=10+2/3n

Solution for 3/5n+15=10+2/3n equation:

3/5n+15=10+2/3n

We move all terms to the left:

3/5n+15-(10+2/3n)=0


Domain of the equation: 5n!=0

n!=0/5

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

3/5n-(2/3n+10)+15=0

We get rid of parentheses

3/5n-2/3n-10+15=0

We calculate fractions


9n/15n^2+(-10n)/15n^2-10+15=0

We add all the numbers together, and all the variables

9n/15n^2+(-10n)/15n^2+5=0

We multiply all the terms by the denominator


9n+(-10n)+5*15n^2=0

Wy multiply elements

75n^2+9n+(-10n)=0

We get rid of parentheses

75n^2+9n-10n=0

We add all the numbers together, and all the variables

75n^2-1n=0

a = 75; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·75·0
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*75}=\frac{0}{150}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*75}=\frac{2}{150}
=1/75
$