0=(20-x)*(300+48*x)

Solution for 0=(20-x)*(300+48*x) equation:

0=(20-x)(300+48x)

We move all terms to the left:

0-((20-x)(300+48x))=0

We add all the numbers together, and all the variables

-((-1x+20)(48x+300))+0=0

We add all the numbers together, and all the variables

-((-1x+20)(48x+300))=0

We multiply parentheses ..

-((-48x^2-300x+960x+6000))=0


We calculate terms in parentheses: -((-48x^2-300x+960x+6000)), so:

(-48x^2-300x+960x+6000)

We get rid of parentheses

-48x^2-300x+960x+6000

We add all the numbers together, and all the variables

-48x^2+660x+6000

Back to the equation:

-(-48x^2+660x+6000)


We get rid of parentheses

48x^2-660x-6000=0

a = 48; b = -660; c = -6000;
Δ = b2-4ac
Δ = -6602-4·48·(-6000)
Δ = 1587600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1587600}=1260$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-660)-1260}{2*48}=\frac{-600}{96}
=-6+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-660)+1260}{2*48}=\frac{1920}{96}
=20
$