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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

2x-3/3x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+3x-3=0

a = 6; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·6·(-3)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*6}=\frac{6}{12}
=1/2
$