1/2n-3/4n=3

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

1/2n-3/4n=3

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We calculate fractions


4n/8n^2+(-6n)/8n^2-3=0

We multiply all the terms by the denominator


4n+(-6n)-3*8n^2=0

Wy multiply elements

-24n^2+4n+(-6n)=0

We get rid of parentheses

-24n^2+4n-6n=0

We add all the numbers together, and all the variables

-24n^2-2n=0

a = -24; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-24)·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*-24}=\frac{0}{-48}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-24}=\frac{4}{-48}
=-1/12
$