F(x)=13/x-3

Solution for F(x)=13/x-3 equation:

(F)=13/F-3

We move all terms to the left:

(F)-(13/F-3)=0


Domain of the equation: F-3)!=0

F∈R


We get rid of parentheses

F-13/F+3=0

We multiply all the terms by the denominator


F*F+3*F-13=0

We add all the numbers together, and all the variables

3F+F*F-13=0

Wy multiply elements

F^2+3F-13=0

a = 1; b = 3; c = -13;
Δ = b2-4ac
Δ = 32-4·1·(-13)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{61}}{2*1}=\frac{-3-\sqrt{61}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{61}}{2*1}=\frac{-3+\sqrt{61}}{2}
$