-5/6x-2/3x=24

Solution for -5/6x-2/3x=24 equation:

-5/6x-2/3x=24

We move all terms to the left:

-5/6x-2/3x-(24)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


(-15x)/18x^2+(-12x)/18x^2-24=0

We multiply all the terms by the denominator


(-15x)+(-12x)-24*18x^2=0

Wy multiply elements

-432x^2+(-15x)+(-12x)=0

We get rid of parentheses

-432x^2-15x-12x=0

We add all the numbers together, and all the variables

-432x^2-27x=0

a = -432; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-432)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-432}=\frac{0}{-864}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-432}=\frac{54}{-864}
=-1/16
$