1/n-3/2n=4

Solution for 1/n-3/2n=4 equation:

1/n-3/2n=4

We move all terms to the left:

1/n-3/2n-(4)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We calculate fractions


2n/2n^2+(-3n)/2n^2-4=0

We multiply all the terms by the denominator


2n+(-3n)-4*2n^2=0

Wy multiply elements

-8n^2+2n+(-3n)=0

We get rid of parentheses

-8n^2+2n-3n=0

We add all the numbers together, and all the variables

-8n^2-1n=0

a = -8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-8)·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*-8}=\frac{0}{-16}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-8}=\frac{2}{-16}
=-1/8
$