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

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

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

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

432y^2-27y=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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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