f(x)=9/x+4

Solution for f(x)=9/x+4 equation:

(F)=9/F+4

We move all terms to the left:

(F)-(9/F+4)=0


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

F∈R


We get rid of parentheses

F-9/F-4=0

We multiply all the terms by the denominator


F*F-4*F-9=0

We add all the numbers together, and all the variables

-4F+F*F-9=0

Wy multiply elements

F^2-4F-9=0

a = 1; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·1·(-9)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{13}}{2*1}=\frac{4-2\sqrt{13}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{13}}{2*1}=\frac{4+2\sqrt{13}}{2}
$