-3p^2+3000p-600000=0

Solution for -3p^2+3000p-600000=0 equation:

-3p^2+3000p-600000=0

a = -3; b = 3000; c = -600000;
Δ = b2-4ac
Δ = 30002-4·(-3)·(-600000)
Δ = 1800000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1800000}=\sqrt{360000*5}=\sqrt{360000}*\sqrt{5}=600\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3000)-600\sqrt{5}}{2*-3}=\frac{-3000-600\sqrt{5}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3000)+600\sqrt{5}}{2*-3}=\frac{-3000+600\sqrt{5}}{-6}
$