X+(64/x)=34

Solution for X+(64/x)=34 equation:

X+(64/X)=34

We move all terms to the left:

X+(64/X)-(34)=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+(+64/X)-34=0

We get rid of parentheses

X+64/X-34=0

We multiply all the terms by the denominator


X*X-34*X+64=0

We add all the numbers together, and all the variables

-34X+X*X+64=0

Wy multiply elements

X^2-34X+64=0

a = 1; b = -34; c = +64;
Δ = b2-4ac
Δ = -342-4·1·64
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-30}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+30}{2*1}=\frac{64}{2}
=32
$