5b*5b-5b-1=0

Solution for 5b*5b-5b-1=0 equation:

5b*5b-5b-1=0

We add all the numbers together, and all the variables

-5b+5b*5b-1=0

Wy multiply elements

25b^2-5b-1=0

a = 25; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·25·(-1)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{5}}{2*25}=\frac{5-5\sqrt{5}}{50}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{5}}{2*25}=\frac{5+5\sqrt{5}}{50}
$