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x+6/x-9=9/x
We move all terms to the left:
x+6/x-9-(9/x)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
x+6/x-(+9/x)-9=0
We get rid of parentheses
x+6/x-9/x-9=0
We multiply all the terms by the denominator
x*x-9*x+6-9=0
We add all the numbers together, and all the variables
-9x+x*x-3=0
Wy multiply elements
x^2-9x-3=0
a = 1; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·1·(-3)
Δ = 93
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{93}}{2*1}=\frac{9-\sqrt{93}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{93}}{2*1}=\frac{9+\sqrt{93}}{2} $
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