200x-1000/200x=0.30

Solution for 200x-1000/200x=0.30 equation:

200x-1000/200x=0.30

We move all terms to the left:

200x-1000/200x-(0.30)=0


Domain of the equation: 200x!=0

x!=0/200

x!=0

x∈R


We add all the numbers together, and all the variables

200x-1000/200x-(0.3)=0

We add all the numbers together, and all the variables

200x-1000/200x-0.3=0

We multiply all the terms by the denominator


200x*200x-(0.3)*200x-1000=0

We multiply parentheses

200x*200x-60x-1000=0

Wy multiply elements

40000x^2-60x-1000=0

a = 40000; b = -60; c = -1000;
Δ = b2-4ac
Δ = -602-4·40000·(-1000)
Δ = 160003600
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:

$\sqrt{\Delta}=\sqrt{160003600}=\sqrt{400*400009}=\sqrt{400}*\sqrt{400009}=20\sqrt{400009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{400009}}{2*40000}=\frac{60-20\sqrt{400009}}{80000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{400009}}{2*40000}=\frac{60+20\sqrt{400009}}{80000}
$