A(w)=-w(w-80)

Solution for A(w)=-w(w-80) equation:

(A)=-A(A-80)

We move all terms to the left:

(A)-(-A(A-80))=0


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

-A(A-80)

We multiply parentheses

-A^2+80A

We add all the numbers together, and all the variables

-1A^2+80A

Back to the equation:

-(-1A^2+80A)


We get rid of parentheses

1A^2-80A+A=0

We add all the numbers together, and all the variables

A^2-79A=0

a = 1; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·1·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*1}=\frac{158}{2}
=79
$