x*(x+x/2)=864

Solution for x*(x+x/2)=864 equation:

x*(x+x/2)=864

We move all terms to the left:

x*(x+x/2)-(864)=0

We add all the numbers together, and all the variables

x*(+x+x/2)-864=0

We multiply parentheses

x^2+x^2-864=0

We add all the numbers together, and all the variables

2x^2-864=0

a = 2; b = 0; c = -864;
Δ = b2-4ac
Δ = 02-4·2·(-864)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*2}=\frac{0-48\sqrt{3}}{4}
=-\frac{48\sqrt{3}}{4}
=-12\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*2}=\frac{0+48\sqrt{3}}{4}
=\frac{48\sqrt{3}}{4}
=12\sqrt{3}
$