-8b*12^.4b=-40

Solution for -8b*12^.4b=-40 equation:

-8b*12^.4b=-40

We move all terms to the left:

-8b*12^.4b-(-40)=0

We add all the numbers together, and all the variables

-8b*12^.4b+40=0

Wy multiply elements

-96b^2+40=0

a = -96; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-96)·40
Δ = 15360
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:

$\sqrt{\Delta}=\sqrt{15360}=\sqrt{1024*15}=\sqrt{1024}*\sqrt{15}=32\sqrt{15}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{15}}{2*-96}=\frac{0-32\sqrt{15}}{-192}
=-\frac{32\sqrt{15}}{-192}
=-\frac{\sqrt{15}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{15}}{2*-96}=\frac{0+32\sqrt{15}}{-192}
=\frac{32\sqrt{15}}{-192}
=\frac{\sqrt{15}}{-6}
$