96=(w-4)w

Solution for 96=(w-4)w equation:

96=(w-4)w

We move all terms to the left:

96-((w-4)w)=0


We calculate terms in parentheses: -((w-4)w), so:

(w-4)w

We multiply parentheses

w^2-4w

Back to the equation:

-(w^2-4w)


We get rid of parentheses

-w^2+4w+96=0

We add all the numbers together, and all the variables

-1w^2+4w+96=0

a = -1; b = 4; c = +96;
Δ = b2-4ac
Δ = 42-4·(-1)·96
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*-1}=\frac{-24}{-2}
=+12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-1}=\frac{16}{-2}
=-8
$