F(x)=6+91/x

Solution for F(x)=6+91/x equation:

(F)=6+91/F

We move all terms to the left:

(F)-(6+91/F)=0


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(91/F+6)=0

We get rid of parentheses

F-91/F-6=0

We multiply all the terms by the denominator


F*F-6*F-91=0

We add all the numbers together, and all the variables

-6F+F*F-91=0

Wy multiply elements

F^2-6F-91=0

a = 1; b = -6; c = -91;
Δ = b2-4ac
Δ = -62-4·1·(-91)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-20}{2*1}=\frac{-14}{2}
=-7
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+20}{2*1}=\frac{26}{2}
=13
$