P(X)=(x-1)(x-2)

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

(P)=(P-1)(P-2)

We move all terms to the left:

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

We multiply parentheses ..

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


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

(+P^2-2P-1P+2)

We get rid of parentheses

P^2-2P-1P+2

We add all the numbers together, and all the variables

P^2-3P+2

Back to the equation:

-(P^2-3P+2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-P^2+P+3P-2=0

We add all the numbers together, and all the variables

-1P^2+4P-2=0

a = -1; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·(-1)·(-2)
Δ = 8
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:

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