1/3x-2=7-9/2x

Solution for 1/3x-2=7-9/2x equation:

1/3x-2=7-9/2x

We move all terms to the left:

1/3x-2-(7-9/2x)=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-(-9/2x+7)-2=0

We get rid of parentheses

1/3x+9/2x-7-2=0

We calculate fractions


2x/6x^2+27x/6x^2-7-2=0

We add all the numbers together, and all the variables

2x/6x^2+27x/6x^2-9=0

We multiply all the terms by the denominator


2x+27x-9*6x^2=0

We add all the numbers together, and all the variables

29x-9*6x^2=0

Wy multiply elements

-54x^2+29x=0

a = -54; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-54)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-54}=\frac{-58}{-108}
=29/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-54}=\frac{0}{-108}
=0
$