10^2n=1/1000000

Solution for 10^2n=1/1000000 equation:

10^2n=1/1000000

We move all terms to the left:

10^2n-(1/1000000)=0

We add all the numbers together, and all the variables

10^2n-(+1/1000000)=0

We get rid of parentheses

10^2n-1/1000000=0

We multiply all the terms by the denominator


10^2n*1000000-1=0

Wy multiply elements

10000000n^2-1=0

a = 10000000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·10000000·(-1)
Δ = 40000000
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:

$\sqrt{\Delta}=\sqrt{40000000}=\sqrt{4000000*10}=\sqrt{4000000}*\sqrt{10}=2000\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{10}}{2*10000000}=\frac{0-2000\sqrt{10}}{20000000}
=-\frac{2000\sqrt{10}}{20000000}
=-\frac{\sqrt{10}}{10000}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{10}}{2*10000000}=\frac{0+2000\sqrt{10}}{20000000}
=\frac{2000\sqrt{10}}{20000000}
=\frac{\sqrt{10}}{10000}
$