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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x^2/108x^2+90x/108x^2+(-54x)/108x^2+2=0

We multiply all the terms by the denominator


24x^2+90x+(-54x)+2*108x^2=0

Wy multiply elements

24x^2+216x^2+90x+(-54x)=0

We get rid of parentheses

24x^2+216x^2+90x-54x=0

We add all the numbers together, and all the variables

240x^2+36x=0

a = 240; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·240·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*240}=\frac{-72}{480}
=-3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*240}=\frac{0}{480}
=0
$