X=2y-1/y-8

Solution for X=2y-1/y-8 equation:

X=2X-1/X-8

We move all terms to the left:

X-(2X-1/X-8)=0


Domain of the equation: X-8)!=0

X∈R


We get rid of parentheses

X-2X+1/X+8=0

We multiply all the terms by the denominator


X*X-2X*X+8*X+1=0

We add all the numbers together, and all the variables

8X+X*X-2X*X+1=0

Wy multiply elements

X^2-2X^2+8X+1=0

We add all the numbers together, and all the variables

-1X^2+8X+1=0

a = -1; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-1)·1
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{17}}{2*-1}=\frac{-8-2\sqrt{17}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{17}}{2*-1}=\frac{-8+2\sqrt{17}}{-2}
$