R(x)=-0.06x2+10.2x-50

Solution for R(x)=-0.06x2+10.2x-50 equation:

(R)=-0.06R^2+10.2R-50

We move all terms to the left:

(R)-(-0.06R^2+10.2R-50)=0

We get rid of parentheses

0.06R^2-10.2R+R+50=0

We add all the numbers together, and all the variables

0.06R^2-9.2R+50=0

a = 0.06; b = -9.2; c = +50;
Δ = b2-4ac
Δ = -9.22-4·0.06·50
Δ = 72.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9.2)-\sqrt{72.64}}{2*0.06}=\frac{9.2-\sqrt{72.64}}{0.12}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.2)+\sqrt{72.64}}{2*0.06}=\frac{9.2+\sqrt{72.64}}{0.12}
$