(8-w)(4w-5)=0

Solution for (8-w)(4w-5)=0 equation:

(8-w)(4w-5)=0

We add all the numbers together, and all the variables

(-1w+8)(4w-5)=0

We multiply parentheses ..

(-4w^2+5w+32w-40)=0

We get rid of parentheses

-4w^2+5w+32w-40=0

We add all the numbers together, and all the variables

-4w^2+37w-40=0

a = -4; b = 37; c = -40;
Δ = b2-4ac
Δ = 372-4·(-4)·(-40)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-27}{2*-4}=\frac{-64}{-8}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+27}{2*-4}=\frac{-10}{-8}
=1+1/4
$