y/3y+9y-24=6y-4-8

Solution for y/3y+9y-24=6y-4-8 equation:

y/3y+9y-24=6y-4-8

We move all terms to the left:

y/3y+9y-24-(6y-4-8)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y/3y+9y-(6y-12)-24=0

We add all the numbers together, and all the variables

9y+y/3y-(6y-12)-24=0

We get rid of parentheses

9y+y/3y-6y+12-24=0

We multiply all the terms by the denominator


9y*3y+y-6y*3y+12*3y-24*3y=0

We add all the numbers together, and all the variables

y+9y*3y-6y*3y+12*3y-24*3y=0

Wy multiply elements

27y^2-18y^2+y+36y-72y=0

We add all the numbers together, and all the variables

9y^2-35y=0

a = 9; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·9·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*9}=\frac{0}{18}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*9}=\frac{70}{18}
=3+8/9
$