3/5y-1/3y=4

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

3/5y-1/3y=4

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We calculate fractions


9y/15y^2+(-5y)/15y^2-4=0

We multiply all the terms by the denominator


9y+(-5y)-4*15y^2=0

Wy multiply elements

-60y^2+9y+(-5y)=0

We get rid of parentheses

-60y^2+9y-5y=0

We add all the numbers together, and all the variables

-60y^2+4y=0

a = -60; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-60)·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*-60}=\frac{-8}{-120}
=1/15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-60}=\frac{0}{-120}
=0
$