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

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

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

We move all terms to the left:

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


Domain of the equation: 6(x+6))!=0

x∈R


We calculate fractions


(-72x^2)/216x+108x^2/216x+()/216x+1=0

We multiply all the terms by the denominator


(-72x^2)+108x^2+1*216x+()=0

We add all the numbers together, and all the variables

108x^2+(-72x^2)+1*216x=0

Wy multiply elements

108x^2+(-72x^2)+216x=0

We get rid of parentheses

108x^2-72x^2+216x=0

We add all the numbers together, and all the variables

36x^2+216x=0

a = 36; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·36·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*36}=\frac{-432}{72}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*36}=\frac{0}{72}
=0
$