384=(20-4)(20-2x)(x)

Solution for 384=(20-4)(20-2x)(x) equation:

384=(20-4)(20-2x)(x)

We move all terms to the left:

384-((20-4)(20-2x)(x))=0

We add all the numbers together, and all the variables

-(16(-2x+20)x)+384=0


We calculate terms in parentheses: -(16(-2x+20)x), so:

16(-2x+20)x

We multiply parentheses

-32x^2+320x

Back to the equation:

-(-32x^2+320x)


We get rid of parentheses

32x^2-320x+384=0

a = 32; b = -320; c = +384;
Δ = b2-4ac
Δ = -3202-4·32·384
Δ = 53248
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:

$\sqrt{\Delta}=\sqrt{53248}=\sqrt{4096*13}=\sqrt{4096}*\sqrt{13}=64\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-64\sqrt{13}}{2*32}=\frac{320-64\sqrt{13}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+64\sqrt{13}}{2*32}=\frac{320+64\sqrt{13}}{64}
$