P(x)=-14+9x-x^2

Solution for P(x)=-14+9x-x^2 equation:

(P)=-14+9P-P^2

We move all terms to the left:

(P)-(-14+9P-P^2)=0

We get rid of parentheses

P^2-9P+P+14=0

We add all the numbers together, and all the variables

P^2-8P+14=0

a = 1; b = -8; c = +14;
Δ = b2-4ac
Δ = -82-4·1·14
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{2}}{2*1}=\frac{8-2\sqrt{2}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{2}}{2*1}=\frac{8+2\sqrt{2}}{2}
$