20=w(15-w)

Solution for 20=w(15-w) equation:

20=w(15-w)

We move all terms to the left:

20-(w(15-w))=0

We add all the numbers together, and all the variables

-(w(-1w+15))+20=0


We calculate terms in parentheses: -(w(-1w+15)), so:

w(-1w+15)

We multiply parentheses

-1w^2+15w

Back to the equation:

-(-1w^2+15w)


We get rid of parentheses

1w^2-15w+20=0

We add all the numbers together, and all the variables

w^2-15w+20=0

a = 1; b = -15; c = +20;
Δ = b2-4ac
Δ = -152-4·1·20
Δ = 145
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{-(-15)-\sqrt{145}}{2*1}=\frac{15-\sqrt{145}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{145}}{2*1}=\frac{15+\sqrt{145}}{2}
$