R(x)=383x-0.9x^2

Solution for R(x)=383x-0.9x^2 equation:

(R)=383R-0.9R^2

We move all terms to the left:

(R)-(383R-0.9R^2)=0

We get rid of parentheses

0.9R^2-383R+R=0

We add all the numbers together, and all the variables

0.9R^2-382R=0

a = 0.9; b = -382; c = 0;
Δ = b2-4ac
Δ = -3822-4·0.9·0
Δ = 145924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{145924}=382$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-382)-382}{2*0.9}=\frac{0}{1.8}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-382)+382}{2*0.9}=\frac{764}{1.8}
=424+0.79999999999995/1.8
$