1/4n+1/3n+8=22

Solution for 1/4n+1/3n+8=22 equation:

1/4n+1/3n+8=22

We move all terms to the left:

1/4n+1/3n+8-(22)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

1/4n+1/3n-14=0

We calculate fractions


3n/12n^2+4n/12n^2-14=0

We multiply all the terms by the denominator


3n+4n-14*12n^2=0

We add all the numbers together, and all the variables

7n-14*12n^2=0

Wy multiply elements

-168n^2+7n=0

a = -168; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-168)·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*-168}=\frac{-14}{-336}
=1/24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-168}=\frac{0}{-336}
=0
$