0=(400+20x)(60-2x)

Solution for 0=(400+20x)(60-2x) equation:

0=(400+20x)(60-2x)

We move all terms to the left:

0-((400+20x)(60-2x))=0

We add all the numbers together, and all the variables

-((20x+400)(-2x+60))+0=0

We add all the numbers together, and all the variables

-((20x+400)(-2x+60))=0

We multiply parentheses ..

-((-40x^2+1200x-800x+24000))=0


We calculate terms in parentheses: -((-40x^2+1200x-800x+24000)), so:

(-40x^2+1200x-800x+24000)

We get rid of parentheses

-40x^2+1200x-800x+24000

We add all the numbers together, and all the variables

-40x^2+400x+24000

Back to the equation:

-(-40x^2+400x+24000)


We get rid of parentheses

40x^2-400x-24000=0

a = 40; b = -400; c = -24000;
Δ = b2-4ac
Δ = -4002-4·40·(-24000)
Δ = 4000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4000000}=2000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-2000}{2*40}=\frac{-1600}{80}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+2000}{2*40}=\frac{2400}{80}
=30
$