X+7/x=9

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Solution for X+7/x=9 equation: 



X+7/X=9

We move all terms to the left:

X+7/X-(9)=0



Domain of the equation: X!=0

X∈R



We multiply all the terms by the denominator


X*X-9*X+7=0

We add all the numbers together, and all the variables

-9X+X*X+7=0

Wy multiply elements

X^2-9X+7=0

a = 1; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·1·7
Δ = 53
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{53}}{2*1}=\frac{9-\sqrt{53}}{2}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{53}}{2*1}=\frac{9+\sqrt{53}}{2}
$

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