-5/2y+3/2=-1/3y-6

Solution for -5/2y+3/2=-1/3y-6 equation:

-5/2y+3/2=-1/3y-6

We move all terms to the left:

-5/2y+3/2-(-1/3y-6)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-6)!=0

y∈R


We get rid of parentheses

-5/2y+1/3y+6+3/2=0

We calculate fractions


(-15y)/24y^2+8y/24y^2+9y/24y^2+6=0

We multiply all the terms by the denominator


(-15y)+8y+9y+6*24y^2=0

We add all the numbers together, and all the variables

17y+(-15y)+6*24y^2=0

Wy multiply elements

144y^2+17y+(-15y)=0

We get rid of parentheses

144y^2+17y-15y=0

We add all the numbers together, and all the variables

144y^2+2y=0

a = 144; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·144·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*144}=\frac{-4}{288}
=-1/72
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*144}=\frac{0}{288}
=0
$