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

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

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

We move all terms to the left:

2/3x-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

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

We calculate fractions


(-60x^2)/216x^2+144x/216x^2+(-108x)/216x^2-1=0

We multiply all the terms by the denominator


(-60x^2)+144x+(-108x)-1*216x^2=0

Wy multiply elements

(-60x^2)-216x^2+144x+(-108x)=0

We get rid of parentheses

-60x^2-216x^2+144x-108x=0

We add all the numbers together, and all the variables

-276x^2+36x=0

a = -276; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-276)·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*-276}=\frac{-72}{-552}
=3/23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-276}=\frac{0}{-552}
=0
$