x(0.2x)=9504

Solution for x(0.2x)=9504 equation:

x(0.2x)=9504

We move all terms to the left:

x(0.2x)-(9504)=0

We add all the numbers together, and all the variables

x(+0.2x)-9504=0

We multiply parentheses

0x^2-9504=0

We add all the numbers together, and all the variables

x^2-9504=0

a = 1; b = 0; c = -9504;
Δ = b2-4ac
Δ = 02-4·1·(-9504)
Δ = 38016
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:

$\sqrt{\Delta}=\sqrt{38016}=\sqrt{576*66}=\sqrt{576}*\sqrt{66}=24\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{66}}{2*1}=\frac{0-24\sqrt{66}}{2}
=-\frac{24\sqrt{66}}{2}
=-12\sqrt{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{66}}{2*1}=\frac{0+24\sqrt{66}}{2}
=\frac{24\sqrt{66}}{2}
=12\sqrt{66}
$