R=289x-x^2

Solution for R=289x-x^2 equation:

=289R-R^2

We move all terms to the left:

-(289R-R^2)=0

We get rid of parentheses

R^2-289R=0

a = 1; b = -289; c = 0;
Δ = b2-4ac
Δ = -2892-4·1·0
Δ = 83521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{83521}=289$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-289)-289}{2*1}=\frac{0}{2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-289)+289}{2*1}=\frac{578}{2}
=289
$