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

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

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

We move all terms to the left:

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


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 3y-7)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-6y)/27y^2+(-9y)/27y^2+7+3=0

We add all the numbers together, and all the variables

(-6y)/27y^2+(-9y)/27y^2+10=0

We multiply all the terms by the denominator


(-6y)+(-9y)+10*27y^2=0

Wy multiply elements

270y^2+(-6y)+(-9y)=0

We get rid of parentheses

270y^2-6y-9y=0

We add all the numbers together, and all the variables

270y^2-15y=0

a = 270; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·270·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*270}=\frac{0}{540}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*270}=\frac{30}{540}
=1/18
$