75=w(20-w)

Solution for 75=w(20-w) equation:

75=w(20-w)

We move all terms to the left:

75-(w(20-w))=0

We add all the numbers together, and all the variables

-(w(-1w+20))+75=0


We calculate terms in parentheses: -(w(-1w+20)), so:

w(-1w+20)

We multiply parentheses

-1w^2+20w

Back to the equation:

-(-1w^2+20w)


We get rid of parentheses

1w^2-20w+75=0

We add all the numbers together, and all the variables

w^2-20w+75=0

a = 1; b = -20; c = +75;
Δ = b2-4ac
Δ = -202-4·1·75
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{-(-20)-10}{2*1}=\frac{10}{2}
=5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*1}=\frac{30}{2}
=15
$