F(x)=14/x-5

Solution for F(x)=14/x-5 equation:

(F)=14/F-5

We move all terms to the left:

(F)-(14/F-5)=0


Domain of the equation: F-5)!=0

F∈R


We get rid of parentheses

F-14/F+5=0

We multiply all the terms by the denominator


F*F+5*F-14=0

We add all the numbers together, and all the variables

5F+F*F-14=0

Wy multiply elements

F^2+5F-14=0

a = 1; b = 5; c = -14;
Δ = b2-4ac
Δ = 52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*1}=\frac{-14}{2}
=-7
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*1}=\frac{4}{2}
=2
$