x(x+6)=680

Solution for x(x+6)=680 equation:

x(x+6)=680

We move all terms to the left:

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

We multiply parentheses

x^2+6x-680=0

a = 1; b = 6; c = -680;
Δ = b2-4ac
Δ = 62-4·1·(-680)
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{-(6)-2\sqrt{689}}{2*1}=\frac{-6-2\sqrt{689}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{689}}{2*1}=\frac{-6+2\sqrt{689}}{2}
$