2x-16=16/x-20x

Solution for 2x-16=16/x-20x equation:

2x-16=16/x-20x

We move all terms to the left:

2x-16-(16/x-20x)=0


Domain of the equation: x-20x)!=0

x∈R


We add all the numbers together, and all the variables

2x-(-20x+16/x)-16=0

We get rid of parentheses

2x+20x-16/x-16=0

We multiply all the terms by the denominator


2x*x+20x*x-16*x-16=0

We add all the numbers together, and all the variables

-16x+2x*x+20x*x-16=0

Wy multiply elements

2x^2+20x^2-16x-16=0

We add all the numbers together, and all the variables

22x^2-16x-16=0

a = 22; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·22·(-16)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{26}}{2*22}=\frac{16-8\sqrt{26}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{26}}{2*22}=\frac{16+8\sqrt{26}}{44}
$