R=900-0.1x^2

Solution for R=900-0.1x^2 equation:

=900-0.1R^2

We move all terms to the left:

-(900-0.1R^2)=0

We get rid of parentheses

0.1R^2-900=0

a = 0.1; b = 0; c = -900;
Δ = b2-4ac
Δ = 02-4·0.1·(-900)
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*0.1}=\frac{0-6\sqrt{10}}{0.2}
=-\frac{6\sqrt{10}}{0.2}
=-\frac{\sqrt{10}}{0.0333333333333}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*0.1}=\frac{0+6\sqrt{10}}{0.2}
=\frac{6\sqrt{10}}{0.2}
=\frac{\sqrt{10}}{0.0333333333333}
$