2/3n+1/4n=-22

Solution for 2/3n+1/4n=-22 equation:

2/3n+1/4n=-22

We move all terms to the left:

2/3n+1/4n-(-22)=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

2/3n+1/4n+22=0

We calculate fractions


8n/12n^2+3n/12n^2+22=0

We multiply all the terms by the denominator


8n+3n+22*12n^2=0

We add all the numbers together, and all the variables

11n+22*12n^2=0

Wy multiply elements

264n^2+11n=0

a = 264; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·264·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*264}=\frac{-22}{528}
=-1/24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*264}=\frac{0}{528}
=0
$