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

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

/5-Y+3=-3Y/Y-1

We move all terms to the left:

/5-Y+3-(-3Y/Y-1)=0


Domain of the equation: Y-1)!=0

Y∈R


We add all the numbers together, and all the variables

-1Y-(-3Y/Y-1)+3+/5=0

We get rid of parentheses

-1Y+3Y/Y+1+3+/5=0

We calculate fractions


-1Y+15Y/5Y+Y/5Y+1+3=0

We add all the numbers together, and all the variables

-1Y+15Y/5Y+Y/5Y+4=0

We multiply all the terms by the denominator


-1Y*5Y+15Y+Y+4*5Y=0

We add all the numbers together, and all the variables

16Y-1Y*5Y+4*5Y=0

Wy multiply elements

-5Y^2+16Y+20Y=0

We add all the numbers together, and all the variables

-5Y^2+36Y=0

a = -5; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-5)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-5}=\frac{-72}{-10}
=7+1/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-5}=\frac{0}{-10}
=0
$