R=-15p2+300p+12,000

Solution for R=-15p2+300p+12,000 equation:

=-15R^2+300R+12.000

We move all terms to the left:

-(-15R^2+300R+12.000)=0

We get rid of parentheses

15R^2-300R-12.000=0

We add all the numbers together, and all the variables

15R^2-300R-12=0

a = 15; b = -300; c = -12;
Δ = b2-4ac
Δ = -3002-4·15·(-12)
Δ = 90720
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:

$\sqrt{\Delta}=\sqrt{90720}=\sqrt{1296*70}=\sqrt{1296}*\sqrt{70}=36\sqrt{70}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-36\sqrt{70}}{2*15}=\frac{300-36\sqrt{70}}{30}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+36\sqrt{70}}{2*15}=\frac{300+36\sqrt{70}}{30}
$