9y-1/y+8=y+6/y+8

Solution for 9y-1/y+8=y+6/y+8 equation:

9y-1/y+8=y+6/y+8

We move all terms to the left:

9y-1/y+8-(y+6/y+8)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y+8)!=0

y∈R


We get rid of parentheses

9y-1/y-y-6/y-8+8=0

We multiply all the terms by the denominator


9y*y-y*y-8*y+8*y-1-6=0

We add all the numbers together, and all the variables

9y*y-y*y-7=0

Wy multiply elements

9y^2-1y^2-7=0

We add all the numbers together, and all the variables

8y^2-7=0

a = 8; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·8·(-7)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*8}=\frac{0-4\sqrt{14}}{16}
=-\frac{4\sqrt{14}}{16}
=-\frac{\sqrt{14}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*8}=\frac{0+4\sqrt{14}}{16}
=\frac{4\sqrt{14}}{16}
=\frac{\sqrt{14}}{4}
$