1+3b=4b+8b^2

Solution for 1+3b=4b+8b^2 equation:

1+3b=4b+8b^2

We move all terms to the left:

1+3b-(4b+8b^2)=0

We get rid of parentheses

-8b^2-4b+3b+1=0

We add all the numbers together, and all the variables

-8b^2-1b+1=0

a = -8; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-8)·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*-8}=\frac{1-\sqrt{33}}{-16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*-8}=\frac{1+\sqrt{33}}{-16}
$