R=(160-0.20x)x

Solution for R=(160-0.20x)x equation:

=(160-0.20R)R

We move all terms to the left:

-((160-0.20R)R)=0

We add all the numbers together, and all the variables

-((-0.2R+160)R)=0


We calculate terms in parentheses: -((-0.2R+160)R), so:

(-0.2R+160)R

We multiply parentheses

0R^2+160R

We add all the numbers together, and all the variables

R^2+160R

Back to the equation:

-(R^2+160R)


We get rid of parentheses

-R^2-160R=0

We add all the numbers together, and all the variables

-1R^2-160R=0

a = -1; b = -160; c = 0;
Δ = b2-4ac
Δ = -1602-4·(-1)·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-160}{2*-1}=\frac{0}{-2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+160}{2*-1}=\frac{320}{-2}
=-160
$