1600/20x=x

Solution for 1600/20x=x equation:

1600/20x=x

We move all terms to the left:

1600/20x-(x)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1600/20x=0

We multiply all the terms by the denominator


-1x*20x+1600=0

Wy multiply elements

-20x^2+1600=0

a = -20; b = 0; c = +1600;
Δ = b2-4ac
Δ = 02-4·(-20)·1600
Δ = 128000
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:

$\sqrt{\Delta}=\sqrt{128000}=\sqrt{25600*5}=\sqrt{25600}*\sqrt{5}=160\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{5}}{2*-20}=\frac{0-160\sqrt{5}}{-40}
=-\frac{160\sqrt{5}}{-40}
=-\frac{4\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{5}}{2*-20}=\frac{0+160\sqrt{5}}{-40}
=\frac{160\sqrt{5}}{-40}
=\frac{4\sqrt{5}}{-1}
$