X(x+12)=560

Solution for X(x+12)=560 equation:

X(X+12)=560

We move all terms to the left:

X(X+12)-(560)=0

We multiply parentheses

X^2+12X-560=0

a = 1; b = 12; c = -560;
Δ = b2-4ac
Δ = 122-4·1·(-560)
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{149}}{2*1}=\frac{-12-4\sqrt{149}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{149}}{2*1}=\frac{-12+4\sqrt{149}}{2}
$