X+9/x-1=64

Solution for X+9/x-1=64 equation:

X+9/X-1=64

We move all terms to the left:

X+9/X-1-(64)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+9/X-65=0

We multiply all the terms by the denominator


X*X-65*X+9=0

We add all the numbers together, and all the variables

-65X+X*X+9=0

Wy multiply elements

X^2-65X+9=0

a = 1; b = -65; c = +9;
Δ = b2-4ac
Δ = -652-4·1·9
Δ = 4189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4189}}{2*1}=\frac{65-\sqrt{4189}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4189}}{2*1}=\frac{65+\sqrt{4189}}{2}
$