A=w(31-2w)

Solution for A=w(31-2w) equation:

=A(31-2A)

We move all terms to the left:

-(A(31-2A))=0

We add all the numbers together, and all the variables

-(A(-2A+31))=0


We calculate terms in parentheses: -(A(-2A+31)), so:

A(-2A+31)

We multiply parentheses

-2A^2+31A

Back to the equation:

-(-2A^2+31A)


We get rid of parentheses

2A^2-31A=0

a = 2; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·2·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*2}=\frac{62}{4}
=15+1/2
$