50=3x(20-x)2

Solution for 50=3x(20-x)2 equation:

50=3x(20-x)2

We move all terms to the left:

50-(3x(20-x)2)=0

We add all the numbers together, and all the variables

-(3x(-1x+20)2)+50=0


We calculate terms in parentheses: -(3x(-1x+20)2), so:

3x(-1x+20)2

We multiply parentheses

-6x^2+120x

Back to the equation:

-(-6x^2+120x)


We get rid of parentheses

6x^2-120x+50=0

a = 6; b = -120; c = +50;
Δ = b2-4ac
Δ = -1202-4·6·50
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-20\sqrt{33}}{2*6}=\frac{120-20\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+20\sqrt{33}}{2*6}=\frac{120+20\sqrt{33}}{12}
$