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

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

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

We move all terms to the left:

1/3x-3-(-3/2x)=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 get rid of parentheses

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

We calculate fractions


2x/6x^2+9x/6x^2-3=0

We multiply all the terms by the denominator


2x+9x-3*6x^2=0

We add all the numbers together, and all the variables

11x-3*6x^2=0

Wy multiply elements

-18x^2+11x=0

a = -18; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-18)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-18}=\frac{-22}{-36}
=11/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-18}=\frac{0}{-36}
=0
$