x-4=4/3x

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



x-4=4/3x
We move all terms to the left:
x-4-(4/3x)=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)-4=0
We get rid of parentheses
x-4/3x-4=0
We multiply all the terms by the denominator
x*3x-4*3x-4=0
Wy multiply elements
3x^2-12x-4=0
a = 3; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·3·(-4)
Δ = 192
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:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*3}=\frac{12-8\sqrt{3}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*3}=\frac{12+8\sqrt{3}}{6} $

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