R(x)=x(16650-190x)

Solution for R(x)=x(16650-190x) equation:

(R)=R(16650-190R)

We move all terms to the left:

(R)-(R(16650-190R))=0

We add all the numbers together, and all the variables

R-(R(-190R+16650))=0


We calculate terms in parentheses: -(R(-190R+16650)), so:

R(-190R+16650)

We multiply parentheses

-190R^2+16650R

Back to the equation:

-(-190R^2+16650R)


We get rid of parentheses

190R^2-16650R+R=0

We add all the numbers together, and all the variables

190R^2-16649R=0

a = 190; b = -16649; c = 0;
Δ = b2-4ac
Δ = -166492-4·190·0
Δ = 277189201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{277189201}=16649$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16649)-16649}{2*190}=\frac{0}{380}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16649)+16649}{2*190}=\frac{33298}{380}
=87+119/190
$