4/3x=x=10/3

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Solution for 4/3x=x=10/3 equation:



4/3x=x=10/3
We move all terms to the left:
4/3x-(x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+4/3x=0
We multiply all the terms by the denominator
-1x*3x+4=0
Wy multiply elements
-3x^2+4=0
a = -3; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-3)·4
Δ = 48
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:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-3}=\frac{0-4\sqrt{3}}{-6} =-\frac{4\sqrt{3}}{-6} =-\frac{2\sqrt{3}}{-3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-3}=\frac{0+4\sqrt{3}}{-6} =\frac{4\sqrt{3}}{-6} =\frac{2\sqrt{3}}{-3} $

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