3/y2-1=8

Solution for 3/y2-1=8 equation:

3/y2-1=8

We move all terms to the left:

3/y2-1-(8)=0


Domain of the equation: y2!=0

y^2!=0/

y^2!=√0

y!=0

y∈R


We add all the numbers together, and all the variables

3/y2-9=0

We multiply all the terms by the denominator


-9*y2+3=0

We add all the numbers together, and all the variables

-9y^2+3=0

a = -9; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-9)·3
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-9}=\frac{0-6\sqrt{3}}{-18}
=-\frac{6\sqrt{3}}{-18}
=-\frac{\sqrt{3}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-9}=\frac{0+6\sqrt{3}}{-18}
=\frac{6\sqrt{3}}{-18}
=\frac{\sqrt{3}}{-3}
$