440,000=x(30-0.4x)

Solution for 440,000=x(30-0.4x) equation:

440.000=x(30-0.4x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(-0.4x+30))+440.000=0

We add all the numbers together, and all the variables

-(x(-0.4x+30))+440=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+440=0

We add all the numbers together, and all the variables

-1x^2-30x+440=0

a = -1; b = -30; c = +440;
Δ = b2-4ac
Δ = -302-4·(-1)·440
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{665}}{2*-1}=\frac{30-2\sqrt{665}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{665}}{2*-1}=\frac{30+2\sqrt{665}}{-2}
$