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^2-199R-22400=0

a = 100; b = -199; c = -22400;
Δ = b2-4ac
Δ = -1992-4·100·(-22400)
Δ = 8999601
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{-(-199)-\sqrt{8999601}}{2*100}=\frac{199-\sqrt{8999601}}{200}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+\sqrt{8999601}}{2*100}=\frac{199+\sqrt{8999601}}{200}
$