5/2y+31/2=2/3y+5

Solution for 5/2y+31/2=2/3y+5 equation:

5/2y+31/2=2/3y+5

We move all terms to the left:

5/2y+31/2-(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 get rid of parentheses

5/2y-2/3y-5+31/2=0

We calculate fractions


15y/24y^2+(-16y)/24y^2+93y/24y^2-5=0

We multiply all the terms by the denominator


15y+(-16y)+93y-5*24y^2=0

We add all the numbers together, and all the variables

108y+(-16y)-5*24y^2=0

Wy multiply elements

-120y^2+108y+(-16y)=0

We get rid of parentheses

-120y^2+108y-16y=0

We add all the numbers together, and all the variables

-120y^2+92y=0

a = -120; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·(-120)·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*-120}=\frac{-184}{-240}
=23/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*-120}=\frac{0}{-240}
=0
$