x(x+12)=120

Solution for x(x+12)=120 equation:

x(x+12)=120

We move all terms to the left:

x(x+12)-(120)=0

We multiply parentheses

x^2+12x-120=0

a = 1; b = 12; c = -120;
Δ = b2-4ac
Δ = 122-4·1·(-120)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{39}}{2*1}=\frac{-12-4\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{39}}{2*1}=\frac{-12+4\sqrt{39}}{2}
$