1/6x-1/3=10/12x+1

Solution for 1/6x-1/3=10/12x+1 equation:

1/6x-1/3=10/12x+1

We move all terms to the left:

1/6x-1/3-(10/12x+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 12x+1)!=0

x∈R


We get rid of parentheses

1/6x-10/12x-1-1/3=0

We calculate fractions


(-72x^2)/648x^2+108x/648x^2+(-540x)/648x^2-1=0

We multiply all the terms by the denominator


(-72x^2)+108x+(-540x)-1*648x^2=0

Wy multiply elements

(-72x^2)-648x^2+108x+(-540x)=0

We get rid of parentheses

-72x^2-648x^2+108x-540x=0

We add all the numbers together, and all the variables

-720x^2-432x=0

a = -720; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·(-720)·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*-720}=\frac{0}{-1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*-720}=\frac{864}{-1440}
=-3/5
$