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

Solution for (8-w)(4w+1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-4w^2-1w+32w+8)=0

We get rid of parentheses

-4w^2-1w+32w+8=0

We add all the numbers together, and all the variables

-4w^2+31w+8=0

a = -4; b = 31; c = +8;
Δ = b2-4ac
Δ = 312-4·(-4)·8
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-33}{2*-4}=\frac{-64}{-8}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+33}{2*-4}=\frac{2}{-8}
=-1/4
$