b*b=1/125

Solution for b*b=1/125 equation:

b*b=1/125

We move all terms to the left:

b*b-(1/125)=0

We add all the numbers together, and all the variables

b*b-(+1/125)=0

Wy multiply elements

b^2-(+1/125)=0

We get rid of parentheses

b^2-1/125=0

We multiply all the terms by the denominator


b^2*125-1=0

Wy multiply elements

125b^2-1=0

a = 125; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·125·(-1)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{5}}{2*125}=\frac{0-10\sqrt{5}}{250}
=-\frac{10\sqrt{5}}{250}
=-\frac{\sqrt{5}}{25}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{5}}{2*125}=\frac{0+10\sqrt{5}}{250}
=\frac{10\sqrt{5}}{250}
=\frac{\sqrt{5}}{25}
$