40=x*(40-2x)

Solution for 40=x*(40-2x) equation:

40=x(40-2x)

We move all terms to the left:

40-(x(40-2x))=0

We add all the numbers together, and all the variables

-(x(-2x+40))+40=0


We calculate terms in parentheses: -(x(-2x+40)), so:

x(-2x+40)

We multiply parentheses

-2x^2+40x

Back to the equation:

-(-2x^2+40x)


We get rid of parentheses

2x^2-40x+40=0

a = 2; b = -40; c = +40;
Δ = b2-4ac
Δ = -402-4·2·40
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{5}}{2*2}=\frac{40-16\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{5}}{2*2}=\frac{40+16\sqrt{5}}{4}
$