100=x(40-x)

Solution for 100=x(40-x) equation:

100=x(40-x)

We move all terms to the left:

100-(x(40-x))=0

We add all the numbers together, and all the variables

-(x(-1x+40))+100=0


We calculate terms in parentheses: -(x(-1x+40)), so:

x(-1x+40)

We multiply parentheses

-1x^2+40x

Back to the equation:

-(-1x^2+40x)


We get rid of parentheses

1x^2-40x+100=0

We add all the numbers together, and all the variables

x^2-40x+100=0

a = 1; b = -40; c = +100;
Δ = b2-4ac
Δ = -402-4·1·100
Δ = 1200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{3}}{2*1}=\frac{40-20\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{3}}{2*1}=\frac{40+20\sqrt{3}}{2}
$