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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

x^2-2x-x-2-2=0

We add all the numbers together, and all the variables

x^2-3x-4=0

a = 1; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*1}=\frac{8}{2}
=4
$