F(x)=800/x

Solution for F(x)=800/x equation:

(F)=800/F

We move all terms to the left:

(F)-(800/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-(+800/F)=0

We get rid of parentheses

F-800/F=0

We multiply all the terms by the denominator


F*F-800=0

Wy multiply elements

F^2-800=0

a = 1; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·1·(-800)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*1}=\frac{0-40\sqrt{2}}{2}
=-\frac{40\sqrt{2}}{2}
=-20\sqrt{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*1}=\frac{0+40\sqrt{2}}{2}
=\frac{40\sqrt{2}}{2}
=20\sqrt{2}
$