2b+6(b-4)b=8

Solution for 2b+6(b-4)b=8 equation:

2b+6(b-4)b=8

We move all terms to the left:

2b+6(b-4)b-(8)=0

We multiply parentheses

6b^2+2b-24b-8=0

We add all the numbers together, and all the variables

6b^2-22b-8=0

a = 6; b = -22; c = -8;
Δ = b2-4ac
Δ = -222-4·6·(-8)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-26}{2*6}=\frac{-4}{12}
=-1/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+26}{2*6}=\frac{48}{12}
=4
$