16/x=x/4x=

Solution for 16/x=x/4x= equation:

16/x=x/4x=

We move all terms to the left:

16/x-(x/4x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

16/x-(+x/4x)=0

We get rid of parentheses

16/x-x/4x=0

We calculate fractions


(-1x^2)/4x^2+64x/4x^2=0

We multiply all the terms by the denominator


(-1x^2)+64x=0

We get rid of parentheses

-1x^2+64x=0

a = -1; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-1)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-1}=\frac{-128}{-2}
=+64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-1}=\frac{0}{-2}
=0
$