F(x)=1/x-4

Solution for F(x)=1/x-4 equation:

(F)=1/F-4

We move all terms to the left:

(F)-(1/F-4)=0


Domain of the equation: F-4)!=0

F∈R


We get rid of parentheses

F-1/F+4=0

We multiply all the terms by the denominator


F*F+4*F-1=0

We add all the numbers together, and all the variables

4F+F*F-1=0

Wy multiply elements

F^2+4F-1=0

a = 1; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·1·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{5}}{2*1}=\frac{-4-2\sqrt{5}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{5}}{2*1}=\frac{-4+2\sqrt{5}}{2}
$