10/3y-13/30=11/2y

Solution for 10/3y-13/30=11/2y equation:

10/3y-13/30=11/2y

We move all terms to the left:

10/3y-13/30-(11/2y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

10/3y-(+11/2y)-13/30=0

We get rid of parentheses

10/3y-11/2y-13/30=0

We calculate fractions


(-156y^2)/540y^2+1800y/540y^2+(-2970y)/540y^2=0

We multiply all the terms by the denominator


(-156y^2)+1800y+(-2970y)=0

We get rid of parentheses

-156y^2+1800y-2970y=0

We add all the numbers together, and all the variables

-156y^2-1170y=0

a = -156; b = -1170; c = 0;
Δ = b2-4ac
Δ = -11702-4·(-156)·0
Δ = 1368900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1368900}=1170$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1170)-1170}{2*-156}=\frac{0}{-312}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1170)+1170}{2*-156}=\frac{2340}{-312}
=-7+1/2
$