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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

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

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

We get rid of parentheses

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

We calculate fractions


(-24x^2)/108x^2+126x/108x^2+(-54x)/108x^2=0

We multiply all the terms by the denominator


(-24x^2)+126x+(-54x)=0

We get rid of parentheses

-24x^2+126x-54x=0

We add all the numbers together, and all the variables

-24x^2+72x=0

a = -24; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-24)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-24}=\frac{-144}{-48}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-24}=\frac{0}{-48}
=0
$