16/x=18x

Solution for 16/x=18x equation:

16/x=18x

We move all terms to the left:

16/x-(18x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-18x+16/x=0

We multiply all the terms by the denominator


-18x*x+16=0

Wy multiply elements

-18x^2+16=0

a = -18; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-18)·16
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-18}=\frac{0-24\sqrt{2}}{-36}
=-\frac{24\sqrt{2}}{-36}
=-\frac{2\sqrt{2}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-18}=\frac{0+24\sqrt{2}}{-36}
=\frac{24\sqrt{2}}{-36}
=\frac{2\sqrt{2}}{-3}
$