7/n+5=3/5n

Solution for 7/n+5=3/5n equation:

7/n+5=3/5n

We move all terms to the left:

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


Domain of the equation: 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

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

We get rid of parentheses

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

We calculate fractions


35n/5n^2+(-3n)/5n^2+5=0

We multiply all the terms by the denominator


35n+(-3n)+5*5n^2=0

Wy multiply elements

25n^2+35n+(-3n)=0

We get rid of parentheses

25n^2+35n-3n=0

We add all the numbers together, and all the variables

25n^2+32n=0

a = 25; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·25·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*25}=\frac{-64}{50}
=-1+7/25
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*25}=\frac{0}{50}
=0
$