R=-12p2+240p+10,000

Solution for R=-12p2+240p+10,000 equation:

=-12R^2+240R+10.000

We move all terms to the left:

-(-12R^2+240R+10.000)=0

We get rid of parentheses

12R^2-240R-10.000=0

We add all the numbers together, and all the variables

12R^2-240R-10=0

a = 12; b = -240; c = -10;
Δ = b2-4ac
Δ = -2402-4·12·(-10)
Δ = 58080
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:

$\sqrt{\Delta}=\sqrt{58080}=\sqrt{1936*30}=\sqrt{1936}*\sqrt{30}=44\sqrt{30}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-44\sqrt{30}}{2*12}=\frac{240-44\sqrt{30}}{24}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+44\sqrt{30}}{2*12}=\frac{240+44\sqrt{30}}{24}
$