X=600x-2x^2

Solution for X=600x-2x^2 equation:

X=600X-2X^2

We move all terms to the left:

X-(600X-2X^2)=0

We get rid of parentheses

2X^2-600X+X=0

We add all the numbers together, and all the variables

2X^2-599X=0

a = 2; b = -599; c = 0;
Δ = b2-4ac
Δ = -5992-4·2·0
Δ = 358801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{358801}=599$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-599)-599}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-599)+599}{2*2}=\frac{1198}{4}
=299+1/2
$