600=500x-100x^2

Solution for 600=500x-100x^2 equation:

600=500x-100x^2

We move all terms to the left:

600-(500x-100x^2)=0

We get rid of parentheses

100x^2-500x+600=0

a = 100; b = -500; c = +600;
Δ = b2-4ac
Δ = -5002-4·100·600
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-100}{2*100}=\frac{400}{200}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+100}{2*100}=\frac{600}{200}
=3
$