R(x)=(330+15x)(6-0.25x)

Solution for R(x)=(330+15x)(6-0.25x) equation:

(R)=(330+15R)(6-0.25R)

We move all terms to the left:

(R)-((330+15R)(6-0.25R))=0

We add all the numbers together, and all the variables

R-((15R+330)(-0.25R+6))=0

We multiply parentheses ..

-((+0R^2+90R+0R+1980))+R=0


We calculate terms in parentheses: -((+0R^2+90R+0R+1980)), so:

(+0R^2+90R+0R+1980)

We get rid of parentheses

0R^2+90R+0R+1980

We add all the numbers together, and all the variables

R^2+91R+1980

Back to the equation:

-(R^2+91R+1980)


We add all the numbers together, and all the variables

R-(R^2+91R+1980)=0

We get rid of parentheses

-R^2+R-91R-1980=0

We add all the numbers together, and all the variables

-1R^2-90R-1980=0

a = -1; b = -90; c = -1980;
Δ = b2-4ac
Δ = -902-4·(-1)·(-1980)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{5}}{2*-1}=\frac{90-6\sqrt{5}}{-2}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{5}}{2*-1}=\frac{90+6\sqrt{5}}{-2}
$