8b^2=120+16b

Solution for 8b^2=120+16b equation:

8b^2=120+16b

We move all terms to the left:

8b^2-(120+16b)=0

We add all the numbers together, and all the variables

8b^2-(16b+120)=0

We get rid of parentheses

8b^2-16b-120=0

a = 8; b = -16; c = -120;
Δ = b2-4ac
Δ = -162-4·8·(-120)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-64}{2*8}=\frac{-48}{16}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+64}{2*8}=\frac{80}{16}
=5
$