x(2/3x)=1440

Solution for x(2/3x)=1440 equation:

x(2/3x)=1440

We move all terms to the left:

x(2/3x)-(1440)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+2/3x)-1440=0

We multiply parentheses

2x^2-1440=0

a = 2; b = 0; c = -1440;
Δ = b2-4ac
Δ = 02-4·2·(-1440)
Δ = 11520
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:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{5}}{2*2}=\frac{0-48\sqrt{5}}{4}
=-\frac{48\sqrt{5}}{4}
=-12\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{5}}{2*2}=\frac{0+48\sqrt{5}}{4}
=\frac{48\sqrt{5}}{4}
=12\sqrt{5}
$