(7/8)n=63

Solution for (7/8)n=63 equation:

(7/8)n=63

We move all terms to the left:

(7/8)n-(63)=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

(+7/8)n-63=0

We multiply parentheses

7n^2-63=0

a = 7; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·7·(-63)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*7}=\frac{-42}{14}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*7}=\frac{42}{14}
=3
$