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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We get rid of parentheses

-60x^2+144x-108x-1=0

We add all the numbers together, and all the variables

-60x^2+36x-1=0

a = -60; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-60)·(-1)
Δ = 1056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{66}}{2*-60}=\frac{-36-4\sqrt{66}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{66}}{2*-60}=\frac{-36+4\sqrt{66}}{-120}
$