3/4n-1/12n=6

Solution for 3/4n-1/12n=6 equation:

3/4n-1/12n=6

We move all terms to the left:

3/4n-1/12n-(6)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 12n!=0

n!=0/12

n!=0

n∈R


We calculate fractions


36n/48n^2+(-4n)/48n^2-6=0

We multiply all the terms by the denominator


36n+(-4n)-6*48n^2=0

Wy multiply elements

-288n^2+36n+(-4n)=0

We get rid of parentheses

-288n^2+36n-4n=0

We add all the numbers together, and all the variables

-288n^2+32n=0

a = -288; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-288)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-288}=\frac{-64}{-576}
=1/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-288}=\frac{0}{-576}
=0
$