2-1/3n=3+1/4n

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

2-1/3n=3+1/4n

We move all terms to the left:

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

We get rid of parentheses

-1/3n-1/4n-3+2=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-4n)/12n^2+(-3n)/12n^2-1=0

We multiply all the terms by the denominator


(-4n)+(-3n)-1*12n^2=0

Wy multiply elements

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

We get rid of parentheses

-12n^2-4n-3n=0

We add all the numbers together, and all the variables

-12n^2-7n=0

a = -12; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-12)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-12}=\frac{0}{-24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-12}=\frac{14}{-24}
=-7/12
$