7/10n+3/1=3/5n+2

Solution for 7/10n+3/1=3/5n+2 equation:

7/10n+3/1=3/5n+2

We move all terms to the left:

7/10n+3/1-(3/5n+2)=0


Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R



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

n∈R


We add all the numbers together, and all the variables

7/10n-(3/5n+2)=0

We get rid of parentheses

7/10n-3/5n-2=0

We calculate fractions


35n/50n^2+(-30n)/50n^2-2=0

We multiply all the terms by the denominator


35n+(-30n)-2*50n^2=0

Wy multiply elements

-100n^2+35n+(-30n)=0

We get rid of parentheses

-100n^2+35n-30n=0

We add all the numbers together, and all the variables

-100n^2+5n=0

a = -100; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-100)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-100}=\frac{-10}{-200}
=1/20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-100}=\frac{0}{-200}
=0
$