(32/3)n=2/9

Solution for (32/3)n=2/9 equation:

(32/3)n=2/9

We move all terms to the left:

(32/3)n-(2/9)=0


Domain of the equation: 3)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+32/3)n-(+2/9)=0

We multiply parentheses

32n^2-(+2/9)=0

We get rid of parentheses

32n^2-2/9=0

We multiply all the terms by the denominator


32n^2*9-2=0

Wy multiply elements

288n^2-2=0

a = 288; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·288·(-2)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*288}=\frac{-48}{576}
=-1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*288}=\frac{48}{576}
=1/12
$