P(x)=-2(x-3)(x-11)

Solution for P(x)=-2(x-3)(x-11) equation:

(P)=-2(P-3)(P-11)

We move all terms to the left:

(P)-(-2(P-3)(P-11))=0

We multiply parentheses ..

-(-2(+P^2-11P-3P+33))+P=0


We calculate terms in parentheses: -(-2(+P^2-11P-3P+33)), so:

-2(+P^2-11P-3P+33)

We multiply parentheses

-2P^2+22P+6P-66

We add all the numbers together, and all the variables

-2P^2+28P-66

Back to the equation:

-(-2P^2+28P-66)


We get rid of parentheses

2P^2-28P+P+66=0

We add all the numbers together, and all the variables

2P^2-27P+66=0

a = 2; b = -27; c = +66;
Δ = b2-4ac
Δ = -272-4·2·66
Δ = 201
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{-(-27)-\sqrt{201}}{2*2}=\frac{27-\sqrt{201}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{201}}{2*2}=\frac{27+\sqrt{201}}{4}
$