P(x)=4+6x-2x^2

Solution for P(x)=4+6x-2x^2 equation:

(P)=4+6P-2P^2

We move all terms to the left:

(P)-(4+6P-2P^2)=0

We get rid of parentheses

2P^2-6P+P-4=0

We add all the numbers together, and all the variables

2P^2-5P-4=0

a = 2; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·2·(-4)
Δ = 57
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{-(-5)-\sqrt{57}}{2*2}=\frac{5-\sqrt{57}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*2}=\frac{5+\sqrt{57}}{4}
$