x(x+12)=620

Solution for x(x+12)=620 equation:

x(x+12)=620

We move all terms to the left:

x(x+12)-(620)=0

We multiply parentheses

x^2+12x-620=0

a = 1; b = 12; c = -620;
Δ = b2-4ac
Δ = 122-4·1·(-620)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{41}}{2*1}=\frac{-12-8\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{41}}{2*1}=\frac{-12+8\sqrt{41}}{2}
$