-3/2x+2-1/3x=-31

Solution for -3/2x+2-1/3x=-31 equation:

-3/2x+2-1/3x=-31

We move all terms to the left:

-3/2x+2-1/3x-(-31)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-1/3x+33=0

We calculate fractions


(-9x)/6x^2+(-2x)/6x^2+33=0

We multiply all the terms by the denominator


(-9x)+(-2x)+33*6x^2=0

Wy multiply elements

198x^2+(-9x)+(-2x)=0

We get rid of parentheses

198x^2-9x-2x=0

We add all the numbers together, and all the variables

198x^2-11x=0

a = 198; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·198·0
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*198}=\frac{0}{396}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*198}=\frac{22}{396}
=1/18
$