-5(7/8)n=-12

Solution for -5(7/8)n=-12 equation:

-5(7/8)n=-12

We move all terms to the left:

-5(7/8)n-(-12)=0


Domain of the equation: 8)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-5(+7/8)n-(-12)=0

We add all the numbers together, and all the variables

-5(+7/8)n+12=0

We multiply parentheses

-35n^2+12=0

a = -35; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-35)·12
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*-35}=\frac{0-4\sqrt{105}}{-70}
=-\frac{4\sqrt{105}}{-70}
=-\frac{2\sqrt{105}}{-35}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*-35}=\frac{0+4\sqrt{105}}{-70}
=\frac{4\sqrt{105}}{-70}
=\frac{2\sqrt{105}}{-35}
$