(-2/3)n=-14

Solution for (-2/3)n=-14 equation:

(-2/3)n=-14

We move all terms to the left:

(-2/3)n-(-14)=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+14=0

We multiply parentheses

-2n^2+14=0

a = -2; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-2)·14
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-2}=\frac{0-4\sqrt{7}}{-4}
=-\frac{4\sqrt{7}}{-4}
=-\frac{\sqrt{7}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-2}=\frac{0+4\sqrt{7}}{-4}
=\frac{4\sqrt{7}}{-4}
=\frac{\sqrt{7}}{-1}
$