x(300-x)=17600

Solution for x(300-x)=17600 equation:

x(300-x)=17600

We move all terms to the left:

x(300-x)-(17600)=0

We add all the numbers together, and all the variables

x(-1x+300)-17600=0

We multiply parentheses

-1x^2+300x-17600=0

a = -1; b = 300; c = -17600;
Δ = b2-4ac
Δ = 3002-4·(-1)·(-17600)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-140}{2*-1}=\frac{-440}{-2}
=+220
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+140}{2*-1}=\frac{-160}{-2}
=+80
$