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

Solution for (x-2)2-(2-x)(4+x)=0. equation:

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

We add all the numbers together, and all the variables

(x-2)2-(-1x+2)(x+4)=0

We multiply parentheses

2x-(-1x+2)(x+4)-4=0

We multiply parentheses ..

-(-1x^2-4x+2x+8)+2x-4=0

We get rid of parentheses

1x^2+4x-2x+2x-8-4=0

We add all the numbers together, and all the variables

x^2+4x-12=0

a = 1; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*1}=\frac{4}{2}
=2
$