F(x)=8+134/x

Solution for F(x)=8+134/x equation:

(F)=8+134/F

We move all terms to the left:

(F)-(8+134/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-(134/F+8)=0

We get rid of parentheses

F-134/F-8=0

We multiply all the terms by the denominator


F*F-8*F-134=0

We add all the numbers together, and all the variables

-8F+F*F-134=0

Wy multiply elements

F^2-8F-134=0

a = 1; b = -8; c = -134;
Δ = b2-4ac
Δ = -82-4·1·(-134)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10\sqrt{6}}{2*1}=\frac{8-10\sqrt{6}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10\sqrt{6}}{2*1}=\frac{8+10\sqrt{6}}{2}
$