3/2x-1+2/x-1=3

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Solution for 3/2x-1+2/x-1=3 equation: 



3/2x-1+2/x-1=3

We move all terms to the left:

3/2x-1+2/x-1-(3)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R





Domain of the equation: x!=0

x∈R



We add all the numbers together, and all the variables

3/2x+2/x-5=0

We calculate fractions


3x/2x^2+4x/2x^2-5=0

We multiply all the terms by the denominator


3x+4x-5*2x^2=0

We add all the numbers together, and all the variables

7x-5*2x^2=0

Wy multiply elements

-10x^2+7x=0

a = -10; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-10)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-10}=\frac{-14}{-20}
=7/10
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-10}=\frac{0}{-20}
=0
$

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