(x-2)(x+8)=23

Solution for (x-2)(x+8)=23 equation:

(x-2)(x+8)=23

We move all terms to the left:

(x-2)(x+8)-(23)=0

We multiply parentheses ..

(+x^2+8x-2x-16)-23=0

We get rid of parentheses

x^2+8x-2x-16-23=0

We add all the numbers together, and all the variables

x^2+6x-39=0

a = 1; b = 6; c = -39;
Δ = b2-4ac
Δ = 62-4·1·(-39)
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8\sqrt{3}}{2*1}=\frac{-6-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8\sqrt{3}}{2*1}=\frac{-6+8\sqrt{3}}{2}
$