R(x)=50x+.2x^2

Solution for R(x)=50x+.2x^2 equation:

(R)=50R+.2R^2

We move all terms to the left:

(R)-(50R+.2R^2)=0

We get rid of parentheses

-.2R^2-50R+R=0

We add all the numbers together, and all the variables

-0.2R^2-49R=0

a = -0.2; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·(-0.2)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*-0.2}=\frac{0}{-0.4}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*-0.2}=\frac{98}{-0.4}
=-245
$