200=w(30-w)

Solution for 200=w(30-w) equation:

200=w(30-w)

We move all terms to the left:

200-(w(30-w))=0

We add all the numbers together, and all the variables

-(w(-1w+30))+200=0


We calculate terms in parentheses: -(w(-1w+30)), so:

w(-1w+30)

We multiply parentheses

-1w^2+30w

Back to the equation:

-(-1w^2+30w)


We get rid of parentheses

1w^2-30w+200=0

We add all the numbers together, and all the variables

w^2-30w+200=0

a = 1; b = -30; c = +200;
Δ = b2-4ac
Δ = -302-4·1·200
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*1}=\frac{20}{2}
=10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*1}=\frac{40}{2}
=20
$