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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


-x+6x/2x+3x/2x+2=0

We add all the numbers together, and all the variables

-1x+6x/2x+3x/2x+2=0

We multiply all the terms by the denominator


-1x*2x+6x+3x+2*2x=0

We add all the numbers together, and all the variables

9x-1x*2x+2*2x=0

Wy multiply elements

-2x^2+9x+4x=0

We add all the numbers together, and all the variables

-2x^2+13x=0

a = -2; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-2)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-2}=\frac{-26}{-4}
=6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-2}=\frac{0}{-4}
=0
$