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

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

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

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n-2)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


25n/15n^2+(-15n)/15n^2+2+5=0

We add all the numbers together, and all the variables

25n/15n^2+(-15n)/15n^2+7=0

We multiply all the terms by the denominator


25n+(-15n)+7*15n^2=0

Wy multiply elements

105n^2+25n+(-15n)=0

We get rid of parentheses

105n^2+25n-15n=0

We add all the numbers together, and all the variables

105n^2+10n=0

a = 105; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·105·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*105}=\frac{-20}{210}
=-2/21
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*105}=\frac{0}{210}
=0
$