F(x)=20/x

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Solution for F(x)=20/x equation:



(F)=20/F
We move all terms to the left:
(F)-(20/F)=0
Domain of the equation: F)!=0
F!=0/1
F!=0
F∈R
We add all the numbers together, and all the variables
F-(+20/F)=0
We get rid of parentheses
F-20/F=0
We multiply all the terms by the denominator
F*F-20=0
Wy multiply elements
F^2-20=0
a = 1; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·1·(-20)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*1}=\frac{0-4\sqrt{5}}{2} =-\frac{4\sqrt{5}}{2} =-2\sqrt{5} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*1}=\frac{0+4\sqrt{5}}{2} =\frac{4\sqrt{5}}{2} =2\sqrt{5} $

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