7/5n-2=3/2n

Solution for 7/5n-2=3/2n equation:

7/5n-2=3/2n

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


14n/10n^2+(-15n)/10n^2-2=0

We multiply all the terms by the denominator


14n+(-15n)-2*10n^2=0

Wy multiply elements

-20n^2+14n+(-15n)=0

We get rid of parentheses

-20n^2+14n-15n=0

We add all the numbers together, and all the variables

-20n^2-1n=0

a = -20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-20)·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*-20}=\frac{0}{-40}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-20}=\frac{2}{-40}
=-1/20
$