-5/6x-2=x

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

-5/6x-2=x

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-1x*6x-2*6x-5=0

Wy multiply elements

-6x^2-12x-5=0

a = -6; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·(-6)·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{6}}{2*-6}=\frac{12-2\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*-6}=\frac{12+2\sqrt{6}}{-12}
$