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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


108x^2/72x^2+(-168x)/72x^2+84x/72x^2+1=0

We multiply all the terms by the denominator


108x^2+(-168x)+84x+1*72x^2=0

We add all the numbers together, and all the variables

108x^2+84x+(-168x)+1*72x^2=0

Wy multiply elements

108x^2+72x^2+84x+(-168x)=0

We get rid of parentheses

108x^2+72x^2+84x-168x=0

We add all the numbers together, and all the variables

180x^2-84x=0

a = 180; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·180·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*180}=\frac{0}{360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*180}=\frac{168}{360}
=7/15
$