X+26=39/x

Solution for X+26=39/x equation:

X+26=39/X

We move all terms to the left:

X+26-(39/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+39/X)+26=0

We get rid of parentheses

X-39/X+26=0

We multiply all the terms by the denominator


X*X+26*X-39=0

We add all the numbers together, and all the variables

26X+X*X-39=0

Wy multiply elements

X^2+26X-39=0

a = 1; b = 26; c = -39;
Δ = b2-4ac
Δ = 262-4·1·(-39)
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-8\sqrt{13}}{2*1}=\frac{-26-8\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+8\sqrt{13}}{2*1}=\frac{-26+8\sqrt{13}}{2}
$