P(x)=4x^2-25/64

Solution for P(x)=4x^2-25/64 equation:

(P)=4P^2-25/64

We move all terms to the left:

(P)-(4P^2-25/64)=0

We get rid of parentheses

-4P^2+P+25/64=0

We multiply all the terms by the denominator


-4P^2*64+P*64+25=0

Wy multiply elements

-256P^2+64P+25=0

a = -256; b = 64; c = +25;
Δ = b2-4ac
Δ = 642-4·(-256)·25
Δ = 29696
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:

$\sqrt{\Delta}=\sqrt{29696}=\sqrt{1024*29}=\sqrt{1024}*\sqrt{29}=32\sqrt{29}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-32\sqrt{29}}{2*-256}=\frac{-64-32\sqrt{29}}{-512}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+32\sqrt{29}}{2*-256}=\frac{-64+32\sqrt{29}}{-512}
$