P(t)=-t^2+22t+112

Solution for P(t)=-t^2+22t+112 equation:

(P)=-P^2+22P+112

We move all terms to the left:

(P)-(-P^2+22P+112)=0

We get rid of parentheses

P^2-22P+P-112=0

We add all the numbers together, and all the variables

P^2-21P-112=0

a = 1; b = -21; c = -112;
Δ = b2-4ac
Δ = -212-4·1·(-112)
Δ = 889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{889}}{2*1}=\frac{21-\sqrt{889}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{889}}{2*1}=\frac{21+\sqrt{889}}{2}
$