P(3)=2x2+5x+1

Solution for P(3)=2x2+5x+1 equation:

(3)=2P^2+5P+1

We move all terms to the left:

(3)-(2P^2+5P+1)=0

We get rid of parentheses

-2P^2-5P-1+3=0

We add all the numbers together, and all the variables

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

a = -2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-2)·2
Δ = 41
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{41}}{2*-2}=\frac{5-\sqrt{41}}{-4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*-2}=\frac{5+\sqrt{41}}{-4}
$