3x-1=4/3x

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Solution for 3x-1=4/3x equation:



3x-1=4/3x
We move all terms to the left:
3x-1-(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
3x-(+4/3x)-1=0
We get rid of parentheses
3x-4/3x-1=0
We multiply all the terms by the denominator
3x*3x-1*3x-4=0
Wy multiply elements
9x^2-3x-4=0
a = 9; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·9·(-4)
Δ = 153
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:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*9}=\frac{3-3\sqrt{17}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*9}=\frac{3+3\sqrt{17}}{18} $

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