X+4/x=13

Solution for X+4/x=13 equation:

X+4/X=13

We move all terms to the left:

X+4/X-(13)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-13*X+4=0

We add all the numbers together, and all the variables

-13X+X*X+4=0

Wy multiply elements

X^2-13X+4=0

a = 1; b = -13; c = +4;
Δ = b2-4ac
Δ = -132-4·1·4
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{17}}{2*1}=\frac{13-3\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{17}}{2*1}=\frac{13+3\sqrt{17}}{2}
$