x(0.60x)=2160

Solution for x(0.60x)=2160 equation:

x(0.60x)=2160

We move all terms to the left:

x(0.60x)-(2160)=0

We add all the numbers together, and all the variables

x(+0.60x)-2160=0

We multiply parentheses

0x^2-2160=0

We add all the numbers together, and all the variables

x^2-2160=0

a = 1; b = 0; c = -2160;
Δ = b2-4ac
Δ = 02-4·1·(-2160)
Δ = 8640
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:

$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{15}}{2*1}=\frac{0-24\sqrt{15}}{2}
=-\frac{24\sqrt{15}}{2}
=-12\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{15}}{2*1}=\frac{0+24\sqrt{15}}{2}
=\frac{24\sqrt{15}}{2}
=12\sqrt{15}
$