x(x+12)=123

Solution for x(x+12)=123 equation:

x(x+12)=123

We move all terms to the left:

x(x+12)-(123)=0

We multiply parentheses

x^2+12x-123=0

a = 1; b = 12; c = -123;
Δ = b2-4ac
Δ = 122-4·1·(-123)
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{159}}{2*1}=\frac{-12-2\sqrt{159}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{159}}{2*1}=\frac{-12+2\sqrt{159}}{2}
$