x-1/6x=200

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Solution for x-1/6x=200 equation:



x-1/6x=200
We move all terms to the left:
x-1/6x-(200)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We multiply all the terms by the denominator
x*6x-200*6x-1=0
Wy multiply elements
6x^2-1200x-1=0
a = 6; b = -1200; c = -1;
Δ = b2-4ac
Δ = -12002-4·6·(-1)
Δ = 1440024
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:
$\sqrt{\Delta}=\sqrt{1440024}=\sqrt{4*360006}=\sqrt{4}*\sqrt{360006}=2\sqrt{360006}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-2\sqrt{360006}}{2*6}=\frac{1200-2\sqrt{360006}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+2\sqrt{360006}}{2*6}=\frac{1200+2\sqrt{360006}}{12} $

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