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

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

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

We multiply parentheses ..

(+56b^2+35b-24b-15)=0

We get rid of parentheses

56b^2+35b-24b-15=0

We add all the numbers together, and all the variables

56b^2+11b-15=0

a = 56; b = 11; c = -15;
Δ = b2-4ac
Δ = 112-4·56·(-15)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-59}{2*56}=\frac{-70}{112}
=-5/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+59}{2*56}=\frac{48}{112}
=3/7
$