440000=x(30-0.4x)

Solution for 440000=x(30-0.4x) equation:

440000=x(30-0.4x)

We move all terms to the left:

440000-(x(30-0.4x))=0

We add all the numbers together, and all the variables

-(x(-0.4x+30))+440000=0


We calculate terms in parentheses: -(x(-0.4x+30)), so:

x(-0.4x+30)

We multiply parentheses

0x^2+30x

We add all the numbers together, and all the variables

x^2+30x

Back to the equation:

-(x^2+30x)


We get rid of parentheses

-x^2-30x+440000=0

We add all the numbers together, and all the variables

-1x^2-30x+440000=0

a = -1; b = -30; c = +440000;
Δ = b2-4ac
Δ = -302-4·(-1)·440000
Δ = 1760900
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:

$\sqrt{\Delta}=\sqrt{1760900}=\sqrt{100*17609}=\sqrt{100}*\sqrt{17609}=10\sqrt{17609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{17609}}{2*-1}=\frac{30-10\sqrt{17609}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{17609}}{2*-1}=\frac{30+10\sqrt{17609}}{-2}
$