x(28/x)=192

Solution for x(28/x)=192 equation:

x(28/x)=192

We move all terms to the left:

x(28/x)-(192)=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(+28/x)-192=0

We multiply parentheses

28x^2-192=0

a = 28; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·28·(-192)
Δ = 21504
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:

$\sqrt{\Delta}=\sqrt{21504}=\sqrt{1024*21}=\sqrt{1024}*\sqrt{21}=32\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{21}}{2*28}=\frac{0-32\sqrt{21}}{56}
=-\frac{32\sqrt{21}}{56}
=-\frac{4\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{21}}{2*28}=\frac{0+32\sqrt{21}}{56}
=\frac{32\sqrt{21}}{56}
=\frac{4\sqrt{21}}{7}
$