x/2x-5=3x-2

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

x/2x-5=3x-2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+x+4x-10x=0

We add all the numbers together, and all the variables

-6x^2-5x=0

a = -6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-6)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-6}=\frac{10}{-12}
=-5/6
$