(8+w)(5w-9)=0

Solution for (8+w)(5w-9)=0 equation:

(8+w)(5w-9)=0

We add all the numbers together, and all the variables

(w+8)(5w-9)=0

We multiply parentheses ..

(+5w^2-9w+40w-72)=0

We get rid of parentheses

5w^2-9w+40w-72=0

We add all the numbers together, and all the variables

5w^2+31w-72=0

a = 5; b = 31; c = -72;
Δ = b2-4ac
Δ = 312-4·5·(-72)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-49}{2*5}=\frac{-80}{10}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+49}{2*5}=\frac{18}{10}
=1+4/5
$