R(x)=15,000x-3x^2

Solution for R(x)=15,000x-3x^2 equation:

(R)=15.000R-3R^2

We move all terms to the left:

(R)-(15.000R-3R^2)=0

We get rid of parentheses

3R^2-15.000R+R=0

We add all the numbers together, and all the variables

3R^2-14R=0

a = 3; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·3·0
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*3}=\frac{0}{6}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*3}=\frac{28}{6}
=4+2/3
$