(2/3)n-6=22

Solution for (2/3)n-6=22 equation:

(2/3)n-6=22

We move all terms to the left:

(2/3)n-6-(22)=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

(+2/3)n-6-22=0

We add all the numbers together, and all the variables

(+2/3)n-28=0

We multiply parentheses

2n^2-28=0

a = 2; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·2·(-28)
Δ = 224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*2}=\frac{0-4\sqrt{14}}{4}
=-\frac{4\sqrt{14}}{4}
=-\sqrt{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*2}=\frac{0+4\sqrt{14}}{4}
=\frac{4\sqrt{14}}{4}
=\sqrt{14}
$