-7(7/9)n=-7

Solution for -7(7/9)n=-7 equation:

-7(7/9)n=-7

We move all terms to the left:

-7(7/9)n-(-7)=0


Domain of the equation: 9)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-7(+7/9)n-(-7)=0

We add all the numbers together, and all the variables

-7(+7/9)n+7=0

We multiply parentheses

-49n^2+7=0

a = -49; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-49)·7
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{7}}{2*-49}=\frac{0-14\sqrt{7}}{-98}
=-\frac{14\sqrt{7}}{-98}
=-\frac{\sqrt{7}}{-7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{7}}{2*-49}=\frac{0+14\sqrt{7}}{-98}
=\frac{14\sqrt{7}}{-98}
=\frac{\sqrt{7}}{-7}
$