1/3(y)+9=1/5(y)

Solution for 1/3(y)+9=1/5(y) equation:

1/3(y)+9=1/5(y)

We move all terms to the left:

1/3(y)+9-(1/5(y))=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(+1/5y)+9=0

We get rid of parentheses

1/3y-1/5y+9=0

We calculate fractions


5y/15y^2+(-3y)/15y^2+9=0

We multiply all the terms by the denominator


5y+(-3y)+9*15y^2=0

Wy multiply elements

135y^2+5y+(-3y)=0

We get rid of parentheses

135y^2+5y-3y=0

We add all the numbers together, and all the variables

135y^2+2y=0

a = 135; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·135·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*135}=\frac{-4}{270}
=-2/135
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*135}=\frac{0}{270}
=0
$