1/3y+9=3/4y

Solution for 1/3y+9=3/4y equation:

1/3y+9=3/4y

We move all terms to the left:

1/3y+9-(3/4y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(+3/4y)+9=0

We get rid of parentheses

1/3y-3/4y+9=0

We calculate fractions


4y/12y^2+(-9y)/12y^2+9=0

We multiply all the terms by the denominator


4y+(-9y)+9*12y^2=0

Wy multiply elements

108y^2+4y+(-9y)=0

We get rid of parentheses

108y^2+4y-9y=0

We add all the numbers together, and all the variables

108y^2-5y=0

a = 108; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·108·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*108}=\frac{0}{216}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*108}=\frac{10}{216}
=5/108
$