R(x)=123.5x-x^2

Solution for R(x)=123.5x-x^2 equation:

(R)=123.5R-R^2

We move all terms to the left:

(R)-(123.5R-R^2)=0

We get rid of parentheses

R^2-123.5R+R=0

We add all the numbers together, and all the variables

R^2-122.5R=0

a = 1; b = -122.5; c = 0;
Δ = b2-4ac
Δ = -122.52-4·1·0
Δ = 15006.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122.5)-\sqrt{15006.25}}{2*1}=\frac{122.5-\sqrt{15006.25}}{2}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122.5)+\sqrt{15006.25}}{2*1}=\frac{122.5+\sqrt{15006.25}}{2}
$