P(7)=x^2+x+2

Solution for P(7)=x^2+x+2 equation:

(7)=P^2+P+2

We move all terms to the left:

(7)-(P^2+P+2)=0

We get rid of parentheses

-P^2-P-2+7=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-1)·5
Δ = 21
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{-(-1)-\sqrt{21}}{2*-1}=\frac{1-\sqrt{21}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*-1}=\frac{1+\sqrt{21}}{-2}
$