5/2y=8/3y-24

Solution for 5/2y=8/3y-24 equation:

5/2y=8/3y-24

We move all terms to the left:

5/2y-(8/3y-24)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-24)!=0

y∈R


We get rid of parentheses

5/2y-8/3y+24=0

We calculate fractions


15y/6y^2+(-16y)/6y^2+24=0

We multiply all the terms by the denominator


15y+(-16y)+24*6y^2=0

Wy multiply elements

144y^2+15y+(-16y)=0

We get rid of parentheses

144y^2+15y-16y=0

We add all the numbers together, and all the variables

144y^2-1y=0

a = 144; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·144·0
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*144}=\frac{0}{288}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*144}=\frac{2}{288}
=1/144
$