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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-24x^2)/108x^2+90x/108x^2+(-54x)/108x^2-1=0

We multiply all the terms by the denominator


(-24x^2)+90x+(-54x)-1*108x^2=0

Wy multiply elements

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

We get rid of parentheses

-24x^2-108x^2+90x-54x=0

We add all the numbers together, and all the variables

-132x^2+36x=0

a = -132; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-132)·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*-132}=\frac{-72}{-264}
=3/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-132}=\frac{0}{-264}
=0
$