R(x)=(2000x+20x^2)/x

Solution for R(x)=(2000x+20x^2)/x equation:

(R)=(2000R+20R^2)/R

We move all terms to the left:

(R)-((2000R+20R^2)/R)=0


Domain of the equation: R)!=0

R!=0/1

R!=0

R∈R


We multiply all the terms by the denominator


-((2000R+20R^2)+R*R)=0


We calculate terms in parentheses: -((2000R+20R^2)+R*R), so:

(2000R+20R^2)+R*R

Wy multiply elements

(2000R+20R^2)+R^2

We get rid of parentheses

20R^2+R^2+2000R

We add all the numbers together, and all the variables

21R^2+2000R

Back to the equation:

-(21R^2+2000R)


We get rid of parentheses

-21R^2-2000R=0

a = -21; b = -2000; c = 0;
Δ = b2-4ac
Δ = -20002-4·(-21)·0
Δ = 4000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4000000}=2000$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2000)-2000}{2*-21}=\frac{0}{-42}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2000)+2000}{2*-21}=\frac{4000}{-42}
=-95+5/21
$