(9+3b)(5-7b)=0

Solution for (9+3b)(5-7b)=0 equation:

(9+3b)(5-7b)=0

We add all the numbers together, and all the variables

(3b+9)(-7b+5)=0

We multiply parentheses ..

(-21b^2+15b-63b+45)=0

We get rid of parentheses

-21b^2+15b-63b+45=0

We add all the numbers together, and all the variables

-21b^2-48b+45=0

a = -21; b = -48; c = +45;
Δ = b2-4ac
Δ = -482-4·(-21)·45
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-78}{2*-21}=\frac{-30}{-42}
=5/7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+78}{2*-21}=\frac{126}{-42}
=-3
$