P=-15t^2+600t+50

Solution for P=-15t^2+600t+50 equation:

=-15P^2+600P+50

We move all terms to the left:

-(-15P^2+600P+50)=0

We get rid of parentheses

15P^2-600P-50=0

a = 15; b = -600; c = -50;
Δ = b2-4ac
Δ = -6002-4·15·(-50)
Δ = 363000
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:

$\sqrt{\Delta}=\sqrt{363000}=\sqrt{12100*30}=\sqrt{12100}*\sqrt{30}=110\sqrt{30}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-110\sqrt{30}}{2*15}=\frac{600-110\sqrt{30}}{30}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+110\sqrt{30}}{2*15}=\frac{600+110\sqrt{30}}{30}
$