1/3x-3/4+5/6x=-2

Solution for 1/3x-3/4+5/6x=-2 equation:

1/3x-3/4+5/6x=-2

We move all terms to the left:

1/3x-3/4+5/6x-(-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+5/6x+2-3/4=0

We calculate fractions


(-324x^2)/288x^2+96x/288x^2+240x/288x^2+2=0

We multiply all the terms by the denominator


(-324x^2)+96x+240x+2*288x^2=0

We add all the numbers together, and all the variables

(-324x^2)+336x+2*288x^2=0

Wy multiply elements

(-324x^2)+576x^2+336x=0

We get rid of parentheses

-324x^2+576x^2+336x=0

We add all the numbers together, and all the variables

252x^2+336x=0

a = 252; b = 336; c = 0;
Δ = b2-4ac
Δ = 3362-4·252·0
Δ = 112896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{112896}=336$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-336}{2*252}=\frac{-672}{504}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+336}{2*252}=\frac{0}{504}
=0
$