X+2/x-13=6

Solution for X+2/x-13=6 equation:

X+2/X-13=6

We move all terms to the left:

X+2/X-13-(6)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+2/X-19=0

We multiply all the terms by the denominator


X*X-19*X+2=0

We add all the numbers together, and all the variables

-19X+X*X+2=0

Wy multiply elements

X^2-19X+2=0

a = 1; b = -19; c = +2;
Δ = b2-4ac
Δ = -192-4·1·2
Δ = 353
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{353}}{2*1}=\frac{19-\sqrt{353}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{353}}{2*1}=\frac{19+\sqrt{353}}{2}
$