F(x)=1/x-6

Solution for F(x)=1/x-6 equation:

(F)=1/F-6

We move all terms to the left:

(F)-(1/F-6)=0


Domain of the equation: F-6)!=0

F∈R


We get rid of parentheses

F-1/F+6=0

We multiply all the terms by the denominator


F*F+6*F-1=0

We add all the numbers together, and all the variables

6F+F*F-1=0

Wy multiply elements

F^2+6F-1=0

a = 1; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·1·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{10}}{2*1}=\frac{-6-2\sqrt{10}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{10}}{2*1}=\frac{-6+2\sqrt{10}}{2}
$