x=68/4x

Solution for x=68/4x equation:

x=68/4x

We move all terms to the left:

x-(68/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+68/4x)=0

We get rid of parentheses

x-68/4x=0

We multiply all the terms by the denominator


x*4x-68=0

Wy multiply elements

4x^2-68=0

a = 4; b = 0; c = -68;
Δ = b2-4ac
Δ = 02-4·4·(-68)
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{17}}{2*4}=\frac{0-8\sqrt{17}}{8}
=-\frac{8\sqrt{17}}{8}
=-\sqrt{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{17}}{2*4}=\frac{0+8\sqrt{17}}{8}
=\frac{8\sqrt{17}}{8}
=\sqrt{17}
$