1/2y-3/2=-1/3y-3

Solution for 1/2y-3/2=-1/3y-3 equation:

1/2y-3/2=-1/3y-3

We move all terms to the left:

1/2y-3/2-(-1/3y-3)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

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

We calculate fractions


3y/24y^2+8y/24y^2+(-9y)/24y^2+3=0

We multiply all the terms by the denominator


3y+8y+(-9y)+3*24y^2=0

We add all the numbers together, and all the variables

11y+(-9y)+3*24y^2=0

Wy multiply elements

72y^2+11y+(-9y)=0

We get rid of parentheses

72y^2+11y-9y=0

We add all the numbers together, and all the variables

72y^2+2y=0

a = 72; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·72·0
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*72}=\frac{-4}{144}
=-1/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*72}=\frac{0}{144}
=0
$