200x-x2=R(x)

Solution for 200x-x2=R(x) equation:

200x-x2=(x)

We move all terms to the left:

200x-x2-((x))=0

determiningTheFunctionDomain
200x-x2-x=0

We add all the numbers together, and all the variables

-1x^2+199x=0

a = -1; b = 199; c = 0;
Δ = b2-4ac
Δ = 1992-4·(-1)·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(199)-199}{2*-1}=\frac{-398}{-2}
=+199
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(199)+199}{2*-1}=\frac{0}{-2}
=0
$