X+2/x=32

Solution for X+2/x=32 equation:

X+2/X=32

We move all terms to the left:

X+2/X-(32)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-32*X+2=0

We add all the numbers together, and all the variables

-32X+X*X+2=0

Wy multiply elements

X^2-32X+2=0

a = 1; b = -32; c = +2;
Δ = b2-4ac
Δ = -322-4·1·2
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{254}}{2*1}=\frac{32-2\sqrt{254}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{254}}{2*1}=\frac{32+2\sqrt{254}}{2}
$