4+1/3n=12n+4

Solution for 4+1/3n=12n+4 equation:

4+1/3n=12n+4

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

1/3n-12n-4+4=0

We multiply all the terms by the denominator


-12n*3n-4*3n+4*3n+1=0

Wy multiply elements

-36n^2-12n+12n+1=0

We add all the numbers together, and all the variables

-36n^2+1=0

a = -36; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-36)·1
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-36}=\frac{-12}{-72}
=1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-36}=\frac{12}{-72}
=-1/6
$