3/2x+5=1/3x-2

Solution for 3/2x+5=1/3x-2 equation:

3/2x+5=1/3x-2

We move all terms to the left:

3/2x+5-(1/3x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

3/2x-1/3x+2+5=0

We calculate fractions


9x/6x^2+(-2x)/6x^2+2+5=0

We add all the numbers together, and all the variables

9x/6x^2+(-2x)/6x^2+7=0

We multiply all the terms by the denominator


9x+(-2x)+7*6x^2=0

Wy multiply elements

42x^2+9x+(-2x)=0

We get rid of parentheses

42x^2+9x-2x=0

We add all the numbers together, and all the variables

42x^2+7x=0

a = 42; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·42·0
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*42}=\frac{-14}{84}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*42}=\frac{0}{84}
=0
$