R=(1200-60x)(20+2x)

Solution for R=(1200-60x)(20+2x) equation:

=(1200-60R)(20+2R)

We move all terms to the left:

-((1200-60R)(20+2R))=0

We add all the numbers together, and all the variables

-((-60R+1200)(2R+20))=0

We multiply parentheses ..

-((-120R^2-1200R+2400R+24000))=0


We calculate terms in parentheses: -((-120R^2-1200R+2400R+24000)), so:

(-120R^2-1200R+2400R+24000)

We get rid of parentheses

-120R^2-1200R+2400R+24000

We add all the numbers together, and all the variables

-120R^2+1200R+24000

Back to the equation:

-(-120R^2+1200R+24000)


We get rid of parentheses

120R^2-1200R-24000=0

a = 120; b = -1200; c = -24000;
Δ = b2-4ac
Δ = -12002-4·120·(-24000)
Δ = 12960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12960000}=3600$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-3600}{2*120}=\frac{-2400}{240}
=-10
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+3600}{2*120}=\frac{4800}{240}
=20
$