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

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

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

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 4n+1)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


16n/12n^2+(-3n)/12n^2-1+2=0

We add all the numbers together, and all the variables

16n/12n^2+(-3n)/12n^2+1=0

We multiply all the terms by the denominator


16n+(-3n)+1*12n^2=0

Wy multiply elements

12n^2+16n+(-3n)=0

We get rid of parentheses

12n^2+16n-3n=0

We add all the numbers together, and all the variables

12n^2+13n=0

a = 12; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·12·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*12}=\frac{-26}{24}
=-1+1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*12}=\frac{0}{24}
=0
$