1/2-7/9y-4/9+1/6y=0

Solution for 1/2-7/9y-4/9+1/6y=0 equation:

1/2-7/9y-4/9+1/6y=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We calculate fractions


2916y^2/1944y^2+(-168y)/1944y^2+324y/1944y^2+(-96y)/1944y^2=0

We multiply all the terms by the denominator


2916y^2+(-168y)+324y+(-96y)=0

We add all the numbers together, and all the variables

2916y^2+324y+(-168y)+(-96y)=0

We get rid of parentheses

2916y^2+324y-168y-96y=0

We add all the numbers together, and all the variables

2916y^2+60y=0

a = 2916; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·2916·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*2916}=\frac{-120}{5832}
=-5/243
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*2916}=\frac{0}{5832}
=0
$