X(x+1)(x-1)=15600

Solution for X(x+1)(x-1)=15600 equation:

X(X+1)(X-1)=15600

We move all terms to the left:

X(X+1)(X-1)-(15600)=0

We use the square of the difference formula

X^2-1-15600=0

We add all the numbers together, and all the variables

X^2-15601=0

a = 1; b = 0; c = -15601;
Δ = b2-4ac
Δ = 02-4·1·(-15601)
Δ = 62404
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:

$\sqrt{\Delta}=\sqrt{62404}=\sqrt{4*15601}=\sqrt{4}*\sqrt{15601}=2\sqrt{15601}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15601}}{2*1}=\frac{0-2\sqrt{15601}}{2}
=-\frac{2\sqrt{15601}}{2}
=-\sqrt{15601}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15601}}{2*1}=\frac{0+2\sqrt{15601}}{2}
=\frac{2\sqrt{15601}}{2}
=\sqrt{15601}
$