R(x)=(13+x)(17,000-1,000x)

Solution for R(x)=(13+x)(17,000-1,000x) equation:

(R)=(13+R)(17.000-1.000R)

We move all terms to the left:

(R)-((13+R)(17.000-1.000R))=0

We add all the numbers together, and all the variables

R-((R+13)(-1R+17))=0

We multiply parentheses ..

-((-1R^2+17R-13R+221))+R=0


We calculate terms in parentheses: -((-1R^2+17R-13R+221)), so:

(-1R^2+17R-13R+221)

We get rid of parentheses

-1R^2+17R-13R+221

We add all the numbers together, and all the variables

-1R^2+4R+221

Back to the equation:

-(-1R^2+4R+221)


We get rid of parentheses

1R^2-4R+R-221=0

We add all the numbers together, and all the variables

R^2-3R-221=0

a = 1; b = -3; c = -221;
Δ = b2-4ac
Δ = -32-4·1·(-221)
Δ = 893
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{-(-3)-\sqrt{893}}{2*1}=\frac{3-\sqrt{893}}{2}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{893}}{2*1}=\frac{3+\sqrt{893}}{2}
$