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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


60x^2/216x^2+72x/216x^2+(-108x)/216x^2-1=0

We multiply all the terms by the denominator


60x^2+72x+(-108x)-1*216x^2=0

Wy multiply elements

60x^2-216x^2+72x+(-108x)=0

We get rid of parentheses

60x^2-216x^2+72x-108x=0

We add all the numbers together, and all the variables

-156x^2-36x=0

a = -156; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-156)·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*-156}=\frac{0}{-312}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-156}=\frac{72}{-312}
=-3/13
$