9/10n+3/2=3/5n+1

Solution for 9/10n+3/2=3/5n+1 equation:

9/10n+3/2=3/5n+1

We move all terms to the left:

9/10n+3/2-(3/5n+1)=0


Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R



Domain of the equation: 5n+1)!=0

n∈R


We get rid of parentheses

9/10n-3/5n-1+3/2=0

We calculate fractions


750n^2/200n^2+180n/200n^2+(-120n)/200n^2-1=0

We multiply all the terms by the denominator


750n^2+180n+(-120n)-1*200n^2=0

Wy multiply elements

750n^2-200n^2+180n+(-120n)=0

We get rid of parentheses

750n^2-200n^2+180n-120n=0

We add all the numbers together, and all the variables

550n^2+60n=0

a = 550; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·550·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*550}=\frac{-120}{1100}
=-6/55
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*550}=\frac{0}{1100}
=0
$