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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y+5)!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We calculate fractions


18y^2/72y^2+180y/72y^2+(-48y)/72y^2-5=0

We multiply all the terms by the denominator


18y^2+180y+(-48y)-5*72y^2=0

Wy multiply elements

18y^2-360y^2+180y+(-48y)=0

We get rid of parentheses

18y^2-360y^2+180y-48y=0

We add all the numbers together, and all the variables

-342y^2+132y=0

a = -342; b = 132; c = 0;
Δ = b2-4ac
Δ = 1322-4·(-342)·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-132}{2*-342}=\frac{-264}{-684}
=22/57
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+132}{2*-342}=\frac{0}{-684}
=0
$