x(50-x)=600

Solution for x(50-x)=600 equation:

x(50-x)=600

We move all terms to the left:

x(50-x)-(600)=0

We add all the numbers together, and all the variables

x(-1x+50)-600=0

We multiply parentheses

-1x^2+50x-600=0

a = -1; b = 50; c = -600;
Δ = b2-4ac
Δ = 502-4·(-1)·(-600)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10}{2*-1}=\frac{-60}{-2}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10}{2*-1}=\frac{-40}{-2}
=+20
$