5/x+1/3x=4x/3

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Solution for 5/x+1/3x=4x/3 equation:



5/x+1/3x=4x/3
We move all terms to the left:
5/x+1/3x-(4x/3)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
5/x+1/3x-(+4x/3)=0
We get rid of parentheses
5/x+1/3x-4x/3=0
We calculate fractions
(-4x^2)/27x^2+135x/27x^2+x/27x^2=0
We multiply all the terms by the denominator
(-4x^2)+135x+x=0
We add all the numbers together, and all the variables
(-4x^2)+136x=0
We get rid of parentheses
-4x^2+136x=0
a = -4; b = 136; c = 0;
Δ = b2-4ac
Δ = 1362-4·(-4)·0
Δ = 18496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18496}=136$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-136}{2*-4}=\frac{-272}{-8} =+34 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+136}{2*-4}=\frac{0}{-8} =0 $

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