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

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

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

We move all terms to the left:

1/3x-7/6-(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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-84x^2)/216x^2+72x/216x^2+(-324x)/216x^2=0

We multiply all the terms by the denominator


(-84x^2)+72x+(-324x)=0

We get rid of parentheses

-84x^2+72x-324x=0

We add all the numbers together, and all the variables

-84x^2-252x=0

a = -84; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·(-84)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*-84}=\frac{0}{-168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*-84}=\frac{504}{-168}
=-3
$