x+9/x=9

Solution for x+9/x=9 equation:

x+9/x=9

We move all terms to the left:

x+9/x-(9)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-9*x+9=0

We add all the numbers together, and all the variables

-9x+x*x+9=0

Wy multiply elements

x^2-9x+9=0

a = 1; b = -9; c = +9;
Δ = b2-4ac
Δ = -92-4·1·9
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{5}}{2*1}=\frac{9-3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{5}}{2*1}=\frac{9+3\sqrt{5}}{2}
$