4/5y-5/3=-1/3y-3

Solution for 4/5y-5/3=-1/3y-3 equation:

4/5y-5/3=-1/3y-3

We move all terms to the left:

4/5y-5/3-(-1/3y-3)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



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

y∈R


We get rid of parentheses

4/5y+1/3y+3-5/3=0

We calculate fractions


108y/135y^2+5y/135y^2+(-25y)/135y^2+3=0

We multiply all the terms by the denominator


108y+5y+(-25y)+3*135y^2=0

We add all the numbers together, and all the variables

113y+(-25y)+3*135y^2=0

Wy multiply elements

405y^2+113y+(-25y)=0

We get rid of parentheses

405y^2+113y-25y=0

We add all the numbers together, and all the variables

405y^2+88y=0

a = 405; b = 88; c = 0;
Δ = b2-4ac
Δ = 882-4·405·0
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-88}{2*405}=\frac{-176}{810}
=-88/405
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+88}{2*405}=\frac{0}{810}
=0
$