(x+2)(x-4)=680

Solution for (x+2)(x-4)=680 equation:

(x+2)(x-4)=680

We move all terms to the left:

(x+2)(x-4)-(680)=0

We multiply parentheses ..

(+x^2-4x+2x-8)-680=0

We get rid of parentheses

x^2-4x+2x-8-680=0

We add all the numbers together, and all the variables

x^2-2x-688=0

a = 1; b = -2; c = -688;
Δ = b2-4ac
Δ = -22-4·1·(-688)
Δ = 2756
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:

$\sqrt{\Delta}=\sqrt{2756}=\sqrt{4*689}=\sqrt{4}*\sqrt{689}=2\sqrt{689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{689}}{2*1}=\frac{2-2\sqrt{689}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{689}}{2*1}=\frac{2+2\sqrt{689}}{2}
$