600x-2x^2=(x)

Solution for 600x-2x^2=(x) equation:

600x-2x^2=(x)

We move all terms to the left:

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

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