(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+14X-632=0

a = 1; b = 14; c = -632;
Δ = b2-4ac
Δ = 142-4·1·(-632)
Δ = 2724
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:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{681}}{2*1}=\frac{-14-2\sqrt{681}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{681}}{2*1}=\frac{-14+2\sqrt{681}}{2}
$