x*(4/3x)=192

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Solution for x*(4/3x)=192 equation:



x(4/3x)=192
We move all terms to the left:
x(4/3x)-(192)=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(+4/3x)-192=0
We multiply parentheses
4x^2-192=0
a = 4; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·4·(-192)
Δ = 3072
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:
$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*4}=\frac{0-32\sqrt{3}}{8} =-\frac{32\sqrt{3}}{8} =-4\sqrt{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*4}=\frac{0+32\sqrt{3}}{8} =\frac{32\sqrt{3}}{8} =4\sqrt{3} $

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