-1/3x+2=3/2x-9

Solution for -1/3x+2=3/2x-9 equation:

-1/3x+2=3/2x-9

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-9)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-2x)/6x^2+(-9x)/6x^2+9+2=0

We add all the numbers together, and all the variables

(-2x)/6x^2+(-9x)/6x^2+11=0

We multiply all the terms by the denominator


(-2x)+(-9x)+11*6x^2=0

Wy multiply elements

66x^2+(-2x)+(-9x)=0

We get rid of parentheses

66x^2-2x-9x=0

We add all the numbers together, and all the variables

66x^2-11x=0

a = 66; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·66·0
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*66}=\frac{0}{132}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*66}=\frac{22}{132}
=1/6
$