P=-3t^2+210t-1200

Solution for P=-3t^2+210t-1200 equation:

=-3P^2+210P-1200

We move all terms to the left:

-(-3P^2+210P-1200)=0

We get rid of parentheses

3P^2-210P+1200=0

a = 3; b = -210; c = +1200;
Δ = b2-4ac
Δ = -2102-4·3·1200
Δ = 29700
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:

$\sqrt{\Delta}=\sqrt{29700}=\sqrt{900*33}=\sqrt{900}*\sqrt{33}=30\sqrt{33}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-30\sqrt{33}}{2*3}=\frac{210-30\sqrt{33}}{6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+30\sqrt{33}}{2*3}=\frac{210+30\sqrt{33}}{6}
$