A=w(80+2w)

Solution for A=w(80+2w) equation:

=A(80+2A)

We move all terms to the left:

-(A(80+2A))=0

We add all the numbers together, and all the variables

-(A(2A+80))=0


We calculate terms in parentheses: -(A(2A+80)), so:

A(2A+80)

We multiply parentheses

2A^2+80A

Back to the equation:

-(2A^2+80A)


We get rid of parentheses

-2A^2-80A=0

a = -2; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·(-2)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*-2}=\frac{0}{-4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*-2}=\frac{160}{-4}
=-40
$