3/5y+3=11+1/3y

Solution for 3/5y+3=11+1/3y equation:

3/5y+3=11+1/3y

We move all terms to the left:

3/5y+3-(11+1/3y)=0


Domain of the equation: 5y!=0

y!=0/5

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

3/5y-(1/3y+11)+3=0

We get rid of parentheses

3/5y-1/3y-11+3=0

We calculate fractions


9y/15y^2+(-5y)/15y^2-11+3=0

We add all the numbers together, and all the variables

9y/15y^2+(-5y)/15y^2-8=0

We multiply all the terms by the denominator


9y+(-5y)-8*15y^2=0

Wy multiply elements

-120y^2+9y+(-5y)=0

We get rid of parentheses

-120y^2+9y-5y=0

We add all the numbers together, and all the variables

-120y^2+4y=0

a = -120; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-120)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-120}=\frac{-8}{-240}
=1/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-120}=\frac{0}{-240}
=0
$