R(x)=72x-5x^2

Solution for R(x)=72x-5x^2 equation:

(R)=72R-5R^2

We move all terms to the left:

(R)-(72R-5R^2)=0

We get rid of parentheses

5R^2-72R+R=0

We add all the numbers together, and all the variables

5R^2-71R=0

a = 5; b = -71; c = 0;
Δ = b2-4ac
Δ = -712-4·5·0
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-71}{2*5}=\frac{0}{10}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+71}{2*5}=\frac{142}{10}
=14+1/5
$