X+9/x=7

Solution for X+9/x=7 equation:

X+9/X=7

We move all terms to the left:

X+9/X-(7)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-7*X+9=0

We add all the numbers together, and all the variables

-7X+X*X+9=0

Wy multiply elements

X^2-7X+9=0

a = 1; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·1·9
Δ = 13
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{-(-7)-\sqrt{13}}{2*1}=\frac{7-\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{13}}{2*1}=\frac{7+\sqrt{13}}{2}
$