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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-3x)/18x^2+(-12x)/18x^2-5=0

We multiply all the terms by the denominator


(-3x)+(-12x)-5*18x^2=0

Wy multiply elements

-90x^2+(-3x)+(-12x)=0

We get rid of parentheses

-90x^2-3x-12x=0

We add all the numbers together, and all the variables

-90x^2-15x=0

a = -90; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-90)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-90}=\frac{30}{-180}
=-1/6
$