X(x+2)=123

Solution for X(x+2)=123 equation:

X(X+2)=123

We move all terms to the left:

X(X+2)-(123)=0

We multiply parentheses

X^2+2X-123=0

a = 1; b = 2; c = -123;
Δ = b2-4ac
Δ = 22-4·1·(-123)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{31}}{2*1}=\frac{-2-4\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{31}}{2*1}=\frac{-2+4\sqrt{31}}{2}
$