1/4n+1=2/3n

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

1/4n+1=2/3n

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


3n/12n^2+(-8n)/12n^2+1=0

We multiply all the terms by the denominator


3n+(-8n)+1*12n^2=0

Wy multiply elements

12n^2+3n+(-8n)=0

We get rid of parentheses

12n^2+3n-8n=0

We add all the numbers together, and all the variables

12n^2-5n=0

a = 12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*12}=\frac{0}{24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*12}=\frac{10}{24}
=5/12
$