P(x)=4x(x-2)+4(2x-1)

Solution for P(x)=4x(x-2)+4(2x-1) equation:

(P)=4P(P-2)+4(2P-1)

We move all terms to the left:

(P)-(4P(P-2)+4(2P-1))=0


We calculate terms in parentheses: -(4P(P-2)+4(2P-1)), so:

4P(P-2)+4(2P-1)

We multiply parentheses

4P^2-8P+8P-4

We add all the numbers together, and all the variables

4P^2-4

Back to the equation:

-(4P^2-4)


We get rid of parentheses

-4P^2+P+4=0

a = -4; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-4)·4
Δ = 65
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{65}}{2*-4}=\frac{-1-\sqrt{65}}{-8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*-4}=\frac{-1+\sqrt{65}}{-8}
$