200+1/5x=x

Solution for 200+1/5x=x equation:

200+1/5x=x

We move all terms to the left:

200+1/5x-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/5x+200=0

We multiply all the terms by the denominator


-1x*5x+200*5x+1=0

Wy multiply elements

-5x^2+1000x+1=0

a = -5; b = 1000; c = +1;
Δ = b2-4ac
Δ = 10002-4·(-5)·1
Δ = 1000020
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:

$\sqrt{\Delta}=\sqrt{1000020}=\sqrt{4*250005}=\sqrt{4}*\sqrt{250005}=2\sqrt{250005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-2\sqrt{250005}}{2*-5}=\frac{-1000-2\sqrt{250005}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+2\sqrt{250005}}{2*-5}=\frac{-1000+2\sqrt{250005}}{-10}
$