R(x)=x(15-0.09x)

Solution for R(x)=x(15-0.09x) equation:

(R)=R(15-0.09R)

We move all terms to the left:

(R)-(R(15-0.09R))=0

We add all the numbers together, and all the variables

R-(R(-0.09R+15))=0


We calculate terms in parentheses: -(R(-0.09R+15)), so:

R(-0.09R+15)

We multiply parentheses

0R^2+15R

We add all the numbers together, and all the variables

R^2+15R

Back to the equation:

-(R^2+15R)


We get rid of parentheses

-R^2+R-15R=0

We add all the numbers together, and all the variables

-1R^2-14R=0

a = -1; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-1)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-1}=\frac{0}{-2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-1}=\frac{28}{-2}
=-14
$