3/2y=5/3y+10

Solution for 3/2y=5/3y+10 equation:

3/2y=5/3y+10

We move all terms to the left:

3/2y-(5/3y+10)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y+10)!=0

y∈R


We get rid of parentheses

3/2y-5/3y-10=0

We calculate fractions


9y/6y^2+(-10y)/6y^2-10=0

We multiply all the terms by the denominator


9y+(-10y)-10*6y^2=0

Wy multiply elements

-60y^2+9y+(-10y)=0

We get rid of parentheses

-60y^2+9y-10y=0

We add all the numbers together, and all the variables

-60y^2-1y=0

a = -60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-60}=\frac{2}{-120}
=-1/60
$