1/y-3+1/8=-5/2y-6

Solution for 1/y-3+1/8=-5/2y-6 equation:

1/y-3+1/8=-5/2y-6

We move all terms to the left:

1/y-3+1/8-(-5/2y-6)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y-6)!=0

y∈R


We get rid of parentheses

1/y+5/2y+6-3+1/8=0

We calculate fractions


4y^2/128y^2+128y/128y^2+320y/128y^2+6-3=0

We add all the numbers together, and all the variables

4y^2/128y^2+128y/128y^2+320y/128y^2+3=0

We multiply all the terms by the denominator


4y^2+128y+320y+3*128y^2=0

We add all the numbers together, and all the variables

4y^2+448y+3*128y^2=0

Wy multiply elements

4y^2+384y^2+448y=0

We add all the numbers together, and all the variables

388y^2+448y=0

a = 388; b = 448; c = 0;
Δ = b2-4ac
Δ = 4482-4·388·0
Δ = 200704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{200704}=448$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(448)-448}{2*388}=\frac{-896}{776}
=-1+15/97
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(448)+448}{2*388}=\frac{0}{776}
=0
$