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

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

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

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 10n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


150n^2/200n^2+40n/200n^2+(-60n)/200n^2=0

We multiply all the terms by the denominator


150n^2+40n+(-60n)=0

We get rid of parentheses

150n^2+40n-60n=0

We add all the numbers together, and all the variables

150n^2-20n=0

a = 150; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·150·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*150}=\frac{0}{300}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*150}=\frac{40}{300}
=2/15
$