P(x)=x^2-64

Solution for P(x)=x^2-64 equation:

(P)=P^2-64

We move all terms to the left:

(P)-(P^2-64)=0

We get rid of parentheses

-P^2+P+64=0

We add all the numbers together, and all the variables

-1P^2+P+64=0

a = -1; b = 1; c = +64;
Δ = b2-4ac
Δ = 12-4·(-1)·64
Δ = 257
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{257}}{2*-1}=\frac{-1-\sqrt{257}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*-1}=\frac{-1+\sqrt{257}}{-2}
$