7/3y-2=4/9y

Solution for 7/3y-2=4/9y equation:

7/3y-2=4/9y

We move all terms to the left:

7/3y-2-(4/9y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 9y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

7/3y-(+4/9y)-2=0

We get rid of parentheses

7/3y-4/9y-2=0

We calculate fractions


63y/27y^2+(-12y)/27y^2-2=0

We multiply all the terms by the denominator


63y+(-12y)-2*27y^2=0

Wy multiply elements

-54y^2+63y+(-12y)=0

We get rid of parentheses

-54y^2+63y-12y=0

We add all the numbers together, and all the variables

-54y^2+51y=0

a = -54; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-54)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-54}=\frac{-102}{-108}
=17/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-54}=\frac{0}{-108}
=0
$