x=2000/0.25x

Solution for x=2000/0.25x equation:

x=2000/0.25x

We move all terms to the left:

x-(2000/0.25x)=0


Domain of the equation: 0.25x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+2000/0.25x)=0

We get rid of parentheses

x-2000/0.25x=0

We multiply all the terms by the denominator


x*0.25x-2000=0

Wy multiply elements

0x^2-2000=0

We add all the numbers together, and all the variables

x^2-2000=0

a = 1; b = 0; c = -2000;
Δ = b2-4ac
Δ = 02-4·1·(-2000)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*1}=\frac{0-40\sqrt{5}}{2}
=-\frac{40\sqrt{5}}{2}
=-20\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*1}=\frac{0+40\sqrt{5}}{2}
=\frac{40\sqrt{5}}{2}
=20\sqrt{5}
$