10b=1/10b

Solution for 10b=1/10b equation:

10b=1/10b

We move all terms to the left:

10b-(1/10b)=0


Domain of the equation: 10b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

10b-(+1/10b)=0

We get rid of parentheses

10b-1/10b=0

We multiply all the terms by the denominator


10b*10b-1=0

Wy multiply elements

100b^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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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