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

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

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

We move all terms to the left:

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


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

(-4P^2)+4P

We get rid of parentheses

-4P^2+4P

Back to the equation:

-(-4P^2+4P)


We get rid of parentheses

4P^2-4P+P=0

We add all the numbers together, and all the variables

4P^2-3P=0

a = 4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·4·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*4}=\frac{0}{8}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*4}=\frac{6}{8}
=3/4
$