R=15-9x-3x^2

Solution for R=15-9x-3x^2 equation:

=15-9R-3R^2

We move all terms to the left:

-(15-9R-3R^2)=0

We get rid of parentheses

3R^2+9R-15=0

a = 3; b = 9; c = -15;
Δ = b2-4ac
Δ = 92-4·3·(-15)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{29}}{2*3}=\frac{-9-3\sqrt{29}}{6}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{29}}{2*3}=\frac{-9+3\sqrt{29}}{6}
$