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

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

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

We move all terms to the left:

-4(x-2)-((-2+x)x)=0

We add all the numbers together, and all the variables

-4(x-2)-((x-2)x)=0

We multiply parentheses

-4x-((x-2)x)+8=0


We calculate terms in parentheses: -((x-2)x), so:

(x-2)x

We multiply parentheses

x^2-2x

Back to the equation:

-(x^2-2x)


We get rid of parentheses

-x^2-4x+2x+8=0

We add all the numbers together, and all the variables

-1x^2-2x+8=0

a = -1; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-1}=\frac{8}{-2}
=-4
$