R(x)=(90-x)(400+20x)

Solution for R(x)=(90-x)(400+20x) equation:

(R)=(90-R)(400+20R)

We move all terms to the left:

(R)-((90-R)(400+20R))=0

We add all the numbers together, and all the variables

R-((-1R+90)(20R+400))=0

We multiply parentheses ..

-((-20R^2-400R+1800R+36000))+R=0


We calculate terms in parentheses: -((-20R^2-400R+1800R+36000)), so:

(-20R^2-400R+1800R+36000)

We get rid of parentheses

-20R^2-400R+1800R+36000

We add all the numbers together, and all the variables

-20R^2+1400R+36000

Back to the equation:

-(-20R^2+1400R+36000)


We get rid of parentheses

20R^2-1400R+R-36000=0

We add all the numbers together, and all the variables

20R^2-1399R-36000=0

a = 20; b = -1399; c = -36000;
Δ = b2-4ac
Δ = -13992-4·20·(-36000)
Δ = 4837201
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{-(-1399)-\sqrt{4837201}}{2*20}=\frac{1399-\sqrt{4837201}}{40}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1399)+\sqrt{4837201}}{2*20}=\frac{1399+\sqrt{4837201}}{40}
$