9/y-8y=2

Solution for 9/y-8y=2 equation:

9/y-8y=2

We move all terms to the left:

9/y-8y-(2)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-8y+9/y-2=0

We multiply all the terms by the denominator


-8y*y-2*y+9=0

We add all the numbers together, and all the variables

-2y-8y*y+9=0

Wy multiply elements

-8y^2-2y+9=0

a = -8; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-8)·9
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{73}}{2*-8}=\frac{2-2\sqrt{73}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{73}}{2*-8}=\frac{2+2\sqrt{73}}{-16}
$