10^x=1/10,000,000

Solution for 10^x=1/10,000,000 equation:

10^x=1/10.000.000

We move all terms to the left:

10^x-(1/10.000.000)=0

We add all the numbers together, and all the variables

10^x-(+1/10.000.000)=0

We get rid of parentheses

10^x-1/10.000.000=0

We multiply all the terms by the denominator


10^x*10.000.000-1=0

Wy multiply elements

100x^2-1=0

a = 100; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·100·(-1)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*100}=\frac{-20}{200}
=-1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*100}=\frac{20}{200}
=1/10
$