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

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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 $

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