P=-5t^2+60t-100

Solution for P=-5t^2+60t-100 equation:

=-5P^2+60P-100

We move all terms to the left:

-(-5P^2+60P-100)=0

We get rid of parentheses

5P^2-60P+100=0

a = 5; b = -60; c = +100;
Δ = b2-4ac
Δ = -602-4·5·100
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-40}{2*5}=\frac{20}{10}
=2
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+40}{2*5}=\frac{100}{10}
=10
$