3b(5b+6)+6b(8-3b)=0

Solution for 3b(5b+6)+6b(8-3b)=0 equation:

3b(5b+6)+6b(8-3b)=0

We add all the numbers together, and all the variables

3b(5b+6)+6b(-3b+8)=0

We multiply parentheses

15b^2-18b^2+18b+48b=0

We add all the numbers together, and all the variables

-3b^2+66b=0

a = -3; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-3)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-3}=\frac{-132}{-6}
=+22
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-3}=\frac{0}{-6}
=0
$