(1/3)^3x2=128x

Solution for (1/3)^3x2=128x equation:

(1/3)^3x^2=128x

We move all terms to the left:

(1/3)^3x^2-(128x)=0


Domain of the equation: 3)^3x^2!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)^3x^2-128x=0

We add all the numbers together, and all the variables

-128x+(+1/3)^3x^2=0

We multiply all the terms by the denominator


-128x*3)^3x^2+(+1=0

Wy multiply elements

-384x^2+1=0

a = -384; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-384)·1
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*-384}=\frac{0-16\sqrt{6}}{-768}
=-\frac{16\sqrt{6}}{-768}
=-\frac{\sqrt{6}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*-384}=\frac{0+16\sqrt{6}}{-768}
=\frac{16\sqrt{6}}{-768}
=\frac{\sqrt{6}}{-48}
$