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

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

X/3X-3=-2X-3

We move all terms to the left:

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


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We get rid of parentheses

X/3X+2X+3-3=0

We multiply all the terms by the denominator


X+2X*3X+3*3X-3*3X=0

Wy multiply elements

6X^2+X+9X-9X=0

We add all the numbers together, and all the variables

6X^2+X=0

a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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