80/4x=x

Solution for 80/4x=x equation:

80/4x=x

We move all terms to the left:

80/4x-(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+80/4x=0

We multiply all the terms by the denominator


-1x*4x+80=0

Wy multiply elements

-4x^2+80=0

a = -4; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-4)·80
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*-4}=\frac{0-16\sqrt{5}}{-8}
=-\frac{16\sqrt{5}}{-8}
=-\frac{2\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*-4}=\frac{0+16\sqrt{5}}{-8}
=\frac{16\sqrt{5}}{-8}
=\frac{2\sqrt{5}}{-1}
$