(12/100)n=78

Solution for (12/100)n=78 equation:

(12/100)n=78

We move all terms to the left:

(12/100)n-(78)=0


Domain of the equation: 100)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+12/100)n-78=0

We multiply parentheses

12n^2-78=0

a = 12; b = 0; c = -78;
Δ = b2-4ac
Δ = 02-4·12·(-78)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{26}}{2*12}=\frac{0-12\sqrt{26}}{24}
=-\frac{12\sqrt{26}}{24}
=-\frac{\sqrt{26}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{26}}{2*12}=\frac{0+12\sqrt{26}}{24}
=\frac{12\sqrt{26}}{24}
=\frac{\sqrt{26}}{2}
$