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

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

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

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-48n^2)/48n^2+16n/48n^2+36n/48n^2=0

We multiply all the terms by the denominator


(-48n^2)+16n+36n=0

We add all the numbers together, and all the variables

(-48n^2)+52n=0

We get rid of parentheses

-48n^2+52n=0

a = -48; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-48)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-48}=\frac{-104}{-96}
=1+1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-48}=\frac{0}{-96}
=0
$