2/9y+1/3y=3/7

Solution for 2/9y+1/3y=3/7 equation:

2/9y+1/3y=3/7

We move all terms to the left:

2/9y+1/3y-(3/7)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2/9y+1/3y-(+3/7)=0

We get rid of parentheses

2/9y+1/3y-3/7=0

We calculate fractions


(-243y^2)/1323y^2+294y/1323y^2+441y/1323y^2=0

We multiply all the terms by the denominator


(-243y^2)+294y+441y=0

We add all the numbers together, and all the variables

(-243y^2)+735y=0

We get rid of parentheses

-243y^2+735y=0

a = -243; b = 735; c = 0;
Δ = b2-4ac
Δ = 7352-4·(-243)·0
Δ = 540225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{540225}=735$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(735)-735}{2*-243}=\frac{-1470}{-486}
=3+2/81
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(735)+735}{2*-243}=\frac{0}{-486}
=0
$