R=5.1x-0.03x^2

Solution for R=5.1x-0.03x^2 equation:

=5.1R-0.03R^2

We move all terms to the left:

-(5.1R-0.03R^2)=0

We get rid of parentheses

0.03R^2-5.1R=0

a = 0.03; b = -5.1; c = 0;
Δ = b2-4ac
Δ = -5.12-4·0.03·0
Δ = 26.01
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{-(-5.1)-\sqrt{26.01}}{2*0.03}=\frac{5.1-\sqrt{26.01}}{0.06}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.1)+\sqrt{26.01}}{2*0.03}=\frac{5.1+\sqrt{26.01}}{0.06}
$