0.0683=w(1-0.59w)

Solution for 0.0683=w(1-0.59w) equation:

0.0683=w(1-0.59w)

We move all terms to the left:

0.0683-(w(1-0.59w))=0

We add all the numbers together, and all the variables

-(w(-0.59w+1))+0.0683=0


We calculate terms in parentheses: -(w(-0.59w+1)), so:

w(-0.59w+1)

We multiply parentheses

0w^2+w

We add all the numbers together, and all the variables

w^2+w

Back to the equation:

-(w^2+w)


We get rid of parentheses

-w^2-w+0.0683=0

We add all the numbers together, and all the variables

-1w^2-1w+0.0683=0

a = -1; b = -1; c = +0.0683;
Δ = b2-4ac
Δ = -12-4·(-1)·0.0683
Δ = 1.2732
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1.2732}}{2*-1}=\frac{1-\sqrt{1.2732}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.2732}}{2*-1}=\frac{1+\sqrt{1.2732}}{-2}
$