R(x)=120x-0.1x^2

Solution for R(x)=120x-0.1x^2 equation:

(R)=120R-0.1R^2

We move all terms to the left:

(R)-(120R-0.1R^2)=0

We get rid of parentheses

0.1R^2-120R+R=0

We add all the numbers together, and all the variables

0.1R^2-119R=0

a = 0.1; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·0.1·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*0.1}=\frac{0}{0.2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*0.1}=\frac{238}{0.2}
=1190
$