4b(b+10)-b=10

Solution for 4b(b+10)-b=10 equation:

4b(b+10)-b=10

We move all terms to the left:

4b(b+10)-b-(10)=0

We add all the numbers together, and all the variables

-1b+4b(b+10)-10=0

We multiply parentheses

4b^2-1b+40b-10=0

We add all the numbers together, and all the variables

4b^2+39b-10=0

a = 4; b = 39; c = -10;
Δ = b2-4ac
Δ = 392-4·4·(-10)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-41}{2*4}=\frac{-80}{8}
=-10
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+41}{2*4}=\frac{2}{8}
=1/4
$