5/2y+1=3/y-2

Solution for 5/2y+1=3/y-2 equation:

5/2y+1=3/y-2

We move all terms to the left:

5/2y+1-(3/y-2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y-2)!=0

y∈R


We get rid of parentheses

5/2y-3/y+2+1=0

We calculate fractions


5y/2y^2+(-6y)/2y^2+2+1=0

We add all the numbers together, and all the variables

5y/2y^2+(-6y)/2y^2+3=0

We multiply all the terms by the denominator


5y+(-6y)+3*2y^2=0

Wy multiply elements

6y^2+5y+(-6y)=0

We get rid of parentheses

6y^2+5y-6y=0

We add all the numbers together, and all the variables

6y^2-1y=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$