404/4x=x

Solution for 404/4x=x equation:

404/4x=x

We move all terms to the left:

404/4x-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+404/4x=0

We multiply all the terms by the denominator


-1x*4x+404=0

Wy multiply elements

-4x^2+404=0

a = -4; b = 0; c = +404;
Δ = b2-4ac
Δ = 02-4·(-4)·404
Δ = 6464
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:

$\sqrt{\Delta}=\sqrt{6464}=\sqrt{64*101}=\sqrt{64}*\sqrt{101}=8\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{101}}{2*-4}=\frac{0-8\sqrt{101}}{-8}
=-\frac{8\sqrt{101}}{-8}
=-\frac{\sqrt{101}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{101}}{2*-4}=\frac{0+8\sqrt{101}}{-8}
=\frac{8\sqrt{101}}{-8}
=\frac{\sqrt{101}}{-1}
$