P(x)=9+x-5x^2

Solution for P(x)=9+x-5x^2 equation:

(P)=9+P-5P^2

We move all terms to the left:

(P)-(9+P-5P^2)=0

We get rid of parentheses

5P^2-P+P-9=0

We add all the numbers together, and all the variables

5P^2-9=0

a = 5; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·5·(-9)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*5}=\frac{0-6\sqrt{5}}{10}
=-\frac{6\sqrt{5}}{10}
=-\frac{3\sqrt{5}}{5}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*5}=\frac{0+6\sqrt{5}}{10}
=\frac{6\sqrt{5}}{10}
=\frac{3\sqrt{5}}{5}
$