x(20-x)2=50

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

x(20-x)2=50

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2+40x-50=0

a = -2; b = 40; c = -50;
Δ = b2-4ac
Δ = 402-4·(-2)·(-50)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{3}}{2*-2}=\frac{-40-20\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{3}}{2*-2}=\frac{-40+20\sqrt{3}}{-4}
$