2x-68=256/2x

Solution for 2x-68=256/2x equation:

2x-68=256/2x

We move all terms to the left:

2x-68-(256/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+256/2x)-68=0

We get rid of parentheses

2x-256/2x-68=0

We multiply all the terms by the denominator


2x*2x-68*2x-256=0

Wy multiply elements

4x^2-136x-256=0

a = 4; b = -136; c = -256;
Δ = b2-4ac
Δ = -1362-4·4·(-256)
Δ = 22592
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:

$\sqrt{\Delta}=\sqrt{22592}=\sqrt{64*353}=\sqrt{64}*\sqrt{353}=8\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-8\sqrt{353}}{2*4}=\frac{136-8\sqrt{353}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+8\sqrt{353}}{2*4}=\frac{136+8\sqrt{353}}{8}
$