5b^2=b

Solution for 5b^2=b equation:

5b^2=b

We move all terms to the left:

5b^2-(b)=0

We add all the numbers together, and all the variables

5b^2-1b=0

a = 5; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·5·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*5}=\frac{0}{10}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*5}=\frac{2}{10}
=1/5
$