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0.2=x-200000/x
We move all terms to the left:
0.2-(x-200000/x)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-(+x-200000/x)+0.2=0
We get rid of parentheses
-x+200000/x+0.2=0
We multiply all the terms by the denominator
-x*x+(0.2)*x+200000=0
We multiply parentheses
-x*x+0.2x+200000=0
Wy multiply elements
-1x^2+0.2x+200000=0
a = -1; b = 0.2; c = +200000;
Δ = b2-4ac
Δ = 0.22-4·(-1)·200000
Δ = 800000.04
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.2)-\sqrt{800000.04}}{2*-1}=\frac{-0.2-\sqrt{800000.04}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{800000.04}}{2*-1}=\frac{-0.2+\sqrt{800000.04}}{-2} $
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