F(x)=45/x

Solution for F(x)=45/x equation:

(F)=45/F

We move all terms to the left:

(F)-(45/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-(+45/F)=0

We get rid of parentheses

F-45/F=0

We multiply all the terms by the denominator


F*F-45=0

Wy multiply elements

F^2-45=0

a = 1; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·1·(-45)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*1}=\frac{0-6\sqrt{5}}{2}
=-\frac{6\sqrt{5}}{2}
=-3\sqrt{5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*1}=\frac{0+6\sqrt{5}}{2}
=\frac{6\sqrt{5}}{2}
=3\sqrt{5}
$