1/3n=3+1/4n

Solution for 1/3n=3+1/4n equation:

1/3n=3+1/4n

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 4n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3n-1/4n-3=0

We calculate fractions


4n/12n^2+(-3n)/12n^2-3=0

We multiply all the terms by the denominator


4n+(-3n)-3*12n^2=0

Wy multiply elements

-36n^2+4n+(-3n)=0

We get rid of parentheses

-36n^2+4n-3n=0

We add all the numbers together, and all the variables

-36n^2+n=0

a = -36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-36)·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*-36}=\frac{-2}{-72}
=1/36
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-36}=\frac{0}{-72}
=0
$