P(x)=x^2+4x-8

Solution for P(x)=x^2+4x-8 equation:

(P)=P^2+4P-8

We move all terms to the left:

(P)-(P^2+4P-8)=0

We get rid of parentheses

-P^2+P-4P+8=0

We add all the numbers together, and all the variables

-1P^2-3P+8=0

a = -1; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-1)·8
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{-(-3)-\sqrt{41}}{2*-1}=\frac{3-\sqrt{41}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*-1}=\frac{3+\sqrt{41}}{-2}
$