(3b-5)(8b+7)=0

Solution for (3b-5)(8b+7)=0 equation:

(3b-5)(8b+7)=0

We multiply parentheses ..

(+24b^2+21b-40b-35)=0

We get rid of parentheses

24b^2+21b-40b-35=0

We add all the numbers together, and all the variables

24b^2-19b-35=0

a = 24; b = -19; c = -35;
Δ = b2-4ac
Δ = -192-4·24·(-35)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-61}{2*24}=\frac{-42}{48}
=-7/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+61}{2*24}=\frac{80}{48}
=1+2/3
$