2/3y+1+1/6y=-24

Solution for 2/3y+1+1/6y=-24 equation:

2/3y+1+1/6y=-24

We move all terms to the left:

2/3y+1+1/6y-(-24)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y+1/6y+25=0

We calculate fractions


12y/18y^2+3y/18y^2+25=0

We multiply all the terms by the denominator


12y+3y+25*18y^2=0

We add all the numbers together, and all the variables

15y+25*18y^2=0

Wy multiply elements

450y^2+15y=0

a = 450; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·450·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*450}=\frac{-30}{900}
=-1/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*450}=\frac{0}{900}
=0
$