(r-2)(r+8)=2

Solution for (r-2)(r+8)=2 equation:

(r-2)(r+8)=2

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

r^2+6r-18=0

a = 1; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·1·(-18)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*1}=\frac{-6-6\sqrt{3}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*1}=\frac{-6+6\sqrt{3}}{2}
$