y/5y-3=3y+5

Solution for y/5y-3=3y+5 equation:

y/5y-3=3y+5

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We get rid of parentheses

y/5y-3y-5-3=0

We multiply all the terms by the denominator


y-3y*5y-5*5y-3*5y=0

Wy multiply elements

-15y^2+y-25y-15y=0

We add all the numbers together, and all the variables

-15y^2-39y=0

a = -15; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-15)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-15}=\frac{0}{-30}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-15}=\frac{78}{-30}
=-2+3/5
$