F(x)=-4/x-6

Solution for F(x)=-4/x-6 equation:

(F)=-4/F-6

We move all terms to the left:

(F)-(-4/F-6)=0


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

F∈R


We get rid of parentheses

F+4/F+6=0

We multiply all the terms by the denominator


F*F+6*F+4=0

We add all the numbers together, and all the variables

6F+F*F+4=0

Wy multiply elements

F^2+6F+4=0

a = 1; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·1·4
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{-(6)-2\sqrt{5}}{2*1}=\frac{-6-2\sqrt{5}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*1}=\frac{-6+2\sqrt{5}}{2}
$