3/4n-1/2n=8

Solution for 3/4n-1/2n=8 equation:

3/4n-1/2n=8

We move all terms to the left:

3/4n-1/2n-(8)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We calculate fractions


6n/8n^2+(-4n)/8n^2-8=0

We multiply all the terms by the denominator


6n+(-4n)-8*8n^2=0

Wy multiply elements

-64n^2+6n+(-4n)=0

We get rid of parentheses

-64n^2+6n-4n=0

We add all the numbers together, and all the variables

-64n^2+2n=0

a = -64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-64)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-64}=\frac{-4}{-128}
=1/32
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-64}=\frac{0}{-128}
=0
$