R(x)=120+18x-3x^2

Solution for R(x)=120+18x-3x^2 equation:

(R)=120+18R-3R^2

We move all terms to the left:

(R)-(120+18R-3R^2)=0

We get rid of parentheses

3R^2-18R+R-120=0

We add all the numbers together, and all the variables

3R^2-17R-120=0

a = 3; b = -17; c = -120;
Δ = b2-4ac
Δ = -172-4·3·(-120)
Δ = 1729
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{-(-17)-\sqrt{1729}}{2*3}=\frac{17-\sqrt{1729}}{6}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1729}}{2*3}=\frac{17+\sqrt{1729}}{6}
$