2x-9/3x-2=-3

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

2x-9/3x-2=-3

We move all terms to the left:

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

We multiply all the terms by the denominator


2x*3x+1*3x-9=0

Wy multiply elements

6x^2+3x-9=0

a = 6; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·6·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*6}=\frac{12}{12}
=1
$