(X+8)(x-2)=(x+2)

Solution for (X+8)(x-2)=(x+2) equation:

(X+8)(X-2)=(X+2)

We move all terms to the left:

(X+8)(X-2)-((X+2))=0

We multiply parentheses ..

(+X^2-2X+8X-16)-((X+2))=0


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

(X+2)

We get rid of parentheses

X+2

Back to the equation:

-(X+2)


We get rid of parentheses

X^2-2X+8X-X-16-2=0

We add all the numbers together, and all the variables

X^2+5X-18=0

a = 1; b = 5; c = -18;
Δ = b2-4ac
Δ = 52-4·1·(-18)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*1}=\frac{-5-\sqrt{97}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*1}=\frac{-5+\sqrt{97}}{2}
$