W(x)=x2-2x.W(-2)

Solution for W(x)=x2-2x.W(-2) equation:

(W)=W2-2W.(-2)

We move all terms to the left:

(W)-(W2-2W.(-2))=0


We calculate terms in parentheses: -(W2-2W.(-2)), so:

W2-2W.(-2)

We add all the numbers together, and all the variables

W^2-2W.(-2)

We multiply parentheses

W^2+4W

Back to the equation:

-(W^2+4W)


We get rid of parentheses

-W^2+W-4W=0

We add all the numbers together, and all the variables

-1W^2-3W=0

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

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