1/7n=18n

Solution for 1/7n=18n equation:

1/7n=18n

We move all terms to the left:

1/7n-(18n)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We add all the numbers together, and all the variables

-18n+1/7n=0

We multiply all the terms by the denominator


-18n*7n+1=0

Wy multiply elements

-126n^2+1=0

a = -126; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-126)·1
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*-126}=\frac{0-6\sqrt{14}}{-252}
=-\frac{6\sqrt{14}}{-252}
=-\frac{\sqrt{14}}{-42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*-126}=\frac{0+6\sqrt{14}}{-252}
=\frac{6\sqrt{14}}{-252}
=\frac{\sqrt{14}}{-42}
$