(3/7)n=48

Solution for (3/7)n=48 equation:

(3/7)n=48

We move all terms to the left:

(3/7)n-(48)=0


Domain of the equation: 7)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+3/7)n-48=0

We multiply parentheses

3n^2-48=0

a = 3; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·3·(-48)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*3}=\frac{-24}{6}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*3}=\frac{24}{6}
=4
$