1/3n=16-1/4n

Solution for 1/3n=16-1/4n equation:

1/3n=16-1/4n

We move all terms to the left:

1/3n-(16-1/4n)=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+16)=0

We get rid of parentheses

1/3n+1/4n-16=0

We calculate fractions


4n/12n^2+3n/12n^2-16=0

We multiply all the terms by the denominator


4n+3n-16*12n^2=0

We add all the numbers together, and all the variables

7n-16*12n^2=0

Wy multiply elements

-192n^2+7n=0

a = -192; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-192)·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*-192}=\frac{-14}{-384}
=7/192
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-192}=\frac{0}{-384}
=0
$