2x-5/2x-1=2x-1/3x+2

Solution for 2x-5/2x-1=2x-1/3x+2 equation:

2x-5/2x-1=2x-1/3x+2

We move all terms to the left:

2x-5/2x-1-(2x-1/3x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

2x-5/2x-2x+1/3x-2-1=0

We calculate fractions


2x-2x+(-15x)/6x^2+2x/6x^2-2-1=0

We add all the numbers together, and all the variables

(-15x)/6x^2+2x/6x^2-3=0

We multiply all the terms by the denominator


(-15x)+2x-3*6x^2=0

We add all the numbers together, and all the variables

2x+(-15x)-3*6x^2=0

Wy multiply elements

-18x^2+2x+(-15x)=0

We get rid of parentheses

-18x^2+2x-15x=0

We add all the numbers together, and all the variables

-18x^2-13x=0

a = -18; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-18)·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*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-18}=\frac{26}{-36}
=-13/18
$