P(x)=0.5x^2+8x-9

Solution for P(x)=0.5x^2+8x-9 equation:

(P)=0.5P^2+8P-9

We move all terms to the left:

(P)-(0.5P^2+8P-9)=0

We get rid of parentheses

-0.5P^2+P-8P+9=0

We add all the numbers together, and all the variables

-0.5P^2-7P+9=0

a = -0.5; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·(-0.5)·9
Δ = 67
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{-(-7)-\sqrt{67}}{2*-0.5}=\frac{7-\sqrt{67}}{-1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{67}}{2*-0.5}=\frac{7+\sqrt{67}}{-1}
$