X+5/x=19

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Solution for X+5/x=19 equation: 



X+5/X=19

We move all terms to the left:

X+5/X-(19)=0



Domain of the equation: X!=0

X∈R



We multiply all the terms by the denominator


X*X-19*X+5=0

We add all the numbers together, and all the variables

-19X+X*X+5=0

Wy multiply elements

X^2-19X+5=0

a = 1; b = -19; c = +5;
Δ = b2-4ac
Δ = -192-4·1·5
Δ = 341
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{-(-19)-\sqrt{341}}{2*1}=\frac{19-\sqrt{341}}{2}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{341}}{2*1}=\frac{19+\sqrt{341}}{2}
$

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