P(x)=5+9x-10x^2

Solution for P(x)=5+9x-10x^2 equation:

(P)=5+9P-10P^2

We move all terms to the left:

(P)-(5+9P-10P^2)=0

We get rid of parentheses

10P^2-9P+P-5=0

We add all the numbers together, and all the variables

10P^2-8P-5=0

a = 10; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·10·(-5)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{66}}{2*10}=\frac{8-2\sqrt{66}}{20}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{66}}{2*10}=\frac{8+2\sqrt{66}}{20}
$