2=x(40-2x)

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

2=x(40-2x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = 2; b = -40; c = +2;
Δ = b2-4ac
Δ = -402-4·2·2
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*2}=\frac{40-12\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*2}=\frac{40+12\sqrt{11}}{4}
$