6b(-3b+8)=16

Solution for 6b(-3b+8)=16 equation:

6b(-3b+8)=16

We move all terms to the left:

6b(-3b+8)-(16)=0

We multiply parentheses

-18b^2+48b-16=0

a = -18; b = 48; c = -16;
Δ = b2-4ac
Δ = 482-4·(-18)·(-16)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{2}}{2*-18}=\frac{-48-24\sqrt{2}}{-36}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{2}}{2*-18}=\frac{-48+24\sqrt{2}}{-36}
$