X+6/x=9

Solution for X+6/x=9 equation:

X+6/X=9

We move all terms to the left:

X+6/X-(9)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-9*X+6=0

We add all the numbers together, and all the variables

-9X+X*X+6=0

Wy multiply elements

X^2-9X+6=0

a = 1; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·1·6
Δ = 57
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{-(-9)-\sqrt{57}}{2*1}=\frac{9-\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*1}=\frac{9+\sqrt{57}}{2}
$