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

Solution for (3b-8)(6b+3)=0 equation:

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

We multiply parentheses ..

(+18b^2+9b-48b-24)=0

We get rid of parentheses

18b^2+9b-48b-24=0

We add all the numbers together, and all the variables

18b^2-39b-24=0

a = 18; b = -39; c = -24;
Δ = b2-4ac
Δ = -392-4·18·(-24)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-57}{2*18}=\frac{-18}{36}
=-1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+57}{2*18}=\frac{96}{36}
=2+2/3
$