6/4y+1=9/9y-6

Solution for 6/4y+1=9/9y-6 equation:

6/4y+1=9/9y-6

We move all terms to the left:

6/4y+1-(9/9y-6)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 9y-6)!=0

y∈R


We get rid of parentheses

6/4y-9/9y+6+1=0

We calculate fractions


54y/36y^2+(-36y)/36y^2+6+1=0

We add all the numbers together, and all the variables

54y/36y^2+(-36y)/36y^2+7=0

We multiply all the terms by the denominator


54y+(-36y)+7*36y^2=0

Wy multiply elements

252y^2+54y+(-36y)=0

We get rid of parentheses

252y^2+54y-36y=0

We add all the numbers together, and all the variables

252y^2+18y=0

a = 252; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·252·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*252}=\frac{-36}{504}
=-1/14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*252}=\frac{0}{504}
=0
$