(-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!=0/1

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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-5/6x-2/3x+24=0

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
$