x(x+x)=15600

Solution for x(x+x)=15600 equation:

x(x+x)=15600

We move all terms to the left:

x(x+x)-(15600)=0

We add all the numbers together, and all the variables

x(+2x)-15600=0

We multiply parentheses

2x^2-15600=0

a = 2; b = 0; c = -15600;
Δ = b2-4ac
Δ = 02-4·2·(-15600)
Δ = 124800
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:

$\sqrt{\Delta}=\sqrt{124800}=\sqrt{1600*78}=\sqrt{1600}*\sqrt{78}=40\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{78}}{2*2}=\frac{0-40\sqrt{78}}{4}
=-\frac{40\sqrt{78}}{4}
=-10\sqrt{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{78}}{2*2}=\frac{0+40\sqrt{78}}{4}
=\frac{40\sqrt{78}}{4}
=10\sqrt{78}
$