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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2x/6x^2+15x/6x^2-2-2=0

We add all the numbers together, and all the variables

2x/6x^2+15x/6x^2-4=0

We multiply all the terms by the denominator


2x+15x-4*6x^2=0

We add all the numbers together, and all the variables

17x-4*6x^2=0

Wy multiply elements

-24x^2+17x=0

a = -24; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-24)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-24}=\frac{-34}{-48}
=17/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-24}=\frac{0}{-48}
=0
$