R(x)=-0.1x^2+30x

Solution for R(x)=-0.1x^2+30x equation:

(R)=-0.1R^2+30R

We move all terms to the left:

(R)-(-0.1R^2+30R)=0

We get rid of parentheses

0.1R^2-30R+R=0

We add all the numbers together, and all the variables

0.1R^2-29R=0

a = 0.1; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·0.1·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*0.1}=\frac{0}{0.2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*0.1}=\frac{58}{0.2}
=290
$