(8-w)(4w+9)=0

Solution for (8-w)(4w+9)=0 equation:

(8-w)(4w+9)=0

We add all the numbers together, and all the variables

(-1w+8)(4w+9)=0

We multiply parentheses ..

(-4w^2-9w+32w+72)=0

We get rid of parentheses

-4w^2-9w+32w+72=0

We add all the numbers together, and all the variables

-4w^2+23w+72=0

a = -4; b = 23; c = +72;
Δ = b2-4ac
Δ = 232-4·(-4)·72
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-41}{2*-4}=\frac{-64}{-8}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+41}{2*-4}=\frac{18}{-8}
=-2+1/4
$