1/y-1+5/12=-2/3y-3

Solution for 1/y-1+5/12=-2/3y-3 equation:

1/y-1+5/12=-2/3y-3

We move all terms to the left:

1/y-1+5/12-(-2/3y-3)=0


Domain of the equation: y!=0

y∈R



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

y∈R


We get rid of parentheses

1/y+2/3y+3-1+5/12=0

We calculate fractions


45y^2/36y^2+36y/36y^2+24y/36y^2+3-1=0

We add all the numbers together, and all the variables

45y^2/36y^2+36y/36y^2+24y/36y^2+2=0

We multiply all the terms by the denominator


45y^2+36y+24y+2*36y^2=0

We add all the numbers together, and all the variables

45y^2+60y+2*36y^2=0

Wy multiply elements

45y^2+72y^2+60y=0

We add all the numbers together, and all the variables

117y^2+60y=0

a = 117; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·117·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*117}=\frac{-120}{234}
=-20/39
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*117}=\frac{0}{234}
=0
$