R=120x-0.5x^2

Solution for R=120x-0.5x^2 equation:

=120R-0.5R^2

We move all terms to the left:

-(120R-0.5R^2)=0

We get rid of parentheses

0.5R^2-120R=0

a = 0.5; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·0.5·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*0.5}=\frac{0}{1}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*0.5}=\frac{240}{1}
=240
$