a(a-2)=(a+4)-(a+2)

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

a(a-2)=(a+4)-(a+2)

We move all terms to the left:

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

We multiply parentheses

a^2-2a-((a+4)-(a+2))=0


We calculate terms in parentheses: -((a+4)-(a+2)), so:

(a+4)-(a+2)

We get rid of parentheses

a-a+4-2

We add all the numbers together, and all the variables

2

Back to the equation:

-(2)


a = 1; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·1·(-2)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*1}=\frac{2-2\sqrt{3}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*1}=\frac{2+2\sqrt{3}}{2}
$