P(x)=-0.5x^2+3-2.5

Solution for P(x)=-0.5x^2+3-2.5 equation:

(P)=-0.5P^2+3-2.5

We move all terms to the left:

(P)-(-0.5P^2+3-2.5)=0

We get rid of parentheses

0.5P^2+P-3+2.5=0

We add all the numbers together, and all the variables

0.5P^2+P-0.5=0

a = 0.5; b = 1; c = -0.5;
Δ = b2-4ac
Δ = 12-4·0.5·(-0.5)
Δ = 2
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{-(1)-\sqrt{2}}{2*0.5}=\frac{-1-\sqrt{2}}{1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2}}{2*0.5}=\frac{-1+\sqrt{2}}{1}
$