3/2x+1=7/6x-3

Solution for 3/2x+1=7/6x-3 equation:

3/2x+1=7/6x-3

We move all terms to the left:

3/2x+1-(7/6x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-3)!=0

x∈R


We get rid of parentheses

3/2x-7/6x+3+1=0

We calculate fractions


18x/12x^2+(-14x)/12x^2+3+1=0

We add all the numbers together, and all the variables

18x/12x^2+(-14x)/12x^2+4=0

We multiply all the terms by the denominator


18x+(-14x)+4*12x^2=0

Wy multiply elements

48x^2+18x+(-14x)=0

We get rid of parentheses

48x^2+18x-14x=0

We add all the numbers together, and all the variables

48x^2+4x=0

a = 48; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·48·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*48}=\frac{-8}{96}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*48}=\frac{0}{96}
=0
$