R(x)=(320+20x)*(70-5x)

Solution for R(x)=(320+20x)*(70-5x) equation:

(R)=(320+20R)(70-5R)

We move all terms to the left:

(R)-((320+20R)(70-5R))=0

We add all the numbers together, and all the variables

R-((20R+320)(-5R+70))=0

We multiply parentheses ..

-((-100R^2+1400R-1600R+22400))+R=0


We calculate terms in parentheses: -((-100R^2+1400R-1600R+22400)), so:

(-100R^2+1400R-1600R+22400)

We get rid of parentheses

-100R^2+1400R-1600R+22400

We add all the numbers together, and all the variables

-100R^2-200R+22400

Back to the equation:

-(-100R^2-200R+22400)


We get rid of parentheses

100R^2+200R+R-22400=0

We add all the numbers together, and all the variables

100R^2+201R-22400=0

a = 100; b = 201; c = -22400;
Δ = b2-4ac
Δ = 2012-4·100·(-22400)
Δ = 9000401
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{-(201)-\sqrt{9000401}}{2*100}=\frac{-201-\sqrt{9000401}}{200}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(201)+\sqrt{9000401}}{2*100}=\frac{-201+\sqrt{9000401}}{200}
$