-5/9y+6=4-4/3y

Solution for -5/9y+6=4-4/3y equation:

-5/9y+6=4-4/3y

We move all terms to the left:

-5/9y+6-(4-4/3y)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-5/9y-(-4/3y+4)+6=0

We get rid of parentheses

-5/9y+4/3y-4+6=0

We calculate fractions


(-15y)/27y^2+36y/27y^2-4+6=0

We add all the numbers together, and all the variables

(-15y)/27y^2+36y/27y^2+2=0

We multiply all the terms by the denominator


(-15y)+36y+2*27y^2=0

We add all the numbers together, and all the variables

36y+(-15y)+2*27y^2=0

Wy multiply elements

54y^2+36y+(-15y)=0

We get rid of parentheses

54y^2+36y-15y=0

We add all the numbers together, and all the variables

54y^2+21y=0

a = 54; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·54·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*54}=\frac{-42}{108}
=-7/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*54}=\frac{0}{108}
=0
$