32=(4+w)*w

Solution for 32=(4+w)*w equation:

32=(4+w)*w

We move all terms to the left:

32-((4+w)*w)=0

We add all the numbers together, and all the variables

-((w+4)*w)+32=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+32=0

We add all the numbers together, and all the variables

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

a = -1; b = -4; c = +32;
Δ = b2-4ac
Δ = -42-4·(-1)·32
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*-1}=\frac{-8}{-2}
=+4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-1}=\frac{16}{-2}
=-8
$