5/2y-9=2/3y

Solution for 5/2y-9=2/3y equation:

5/2y-9=2/3y

We move all terms to the left:

5/2y-9-(2/3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

5/2y-(+2/3y)-9=0

We get rid of parentheses

5/2y-2/3y-9=0

We calculate fractions


15y/6y^2+(-4y)/6y^2-9=0

We multiply all the terms by the denominator


15y+(-4y)-9*6y^2=0

Wy multiply elements

-54y^2+15y+(-4y)=0

We get rid of parentheses

-54y^2+15y-4y=0

We add all the numbers together, and all the variables

-54y^2+11y=0

a = -54; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-54)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-54}=\frac{-22}{-108}
=11/54
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-54}=\frac{0}{-108}
=0
$