P(x)=4x^2-64

Solution for P(x)=4x^2-64 equation:

(P)=4P^2-64

We move all terms to the left:

(P)-(4P^2-64)=0

We get rid of parentheses

-4P^2+P+64=0

a = -4; b = 1; c = +64;
Δ = b2-4ac
Δ = 12-4·(-4)·64
Δ = 1025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{41}}{2*-4}=\frac{-1-5\sqrt{41}}{-8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{41}}{2*-4}=\frac{-1+5\sqrt{41}}{-8}
$