(x-8)*(x+6)=680

Solution for (x-8)*(x+6)=680 equation:

(x-8)(x+6)=680

We move all terms to the left:

(x-8)(x+6)-(680)=0

We multiply parentheses ..

(+x^2+6x-8x-48)-680=0

We get rid of parentheses

x^2+6x-8x-48-680=0

We add all the numbers together, and all the variables

x^2-2x-728=0

a = 1; b = -2; c = -728;
Δ = b2-4ac
Δ = -22-4·1·(-728)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-54}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+54}{2*1}=\frac{56}{2}
=28
$