2/3x-3=-1/2x-6

Solution for 2/3x-3=-1/2x-6 equation:

2/3x-3=-1/2x-6

We move all terms to the left:

2/3x-3-(-1/2x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

2/3x+1/2x+6-3=0

We calculate fractions


4x/6x^2+3x/6x^2+6-3=0

We add all the numbers together, and all the variables

4x/6x^2+3x/6x^2+3=0

We multiply all the terms by the denominator


4x+3x+3*6x^2=0

We add all the numbers together, and all the variables

7x+3*6x^2=0

Wy multiply elements

18x^2+7x=0

a = 18; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·18·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*18}=\frac{-14}{36}
=-7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*18}=\frac{0}{36}
=0
$