8+2/f+f=44

Solution for 8+2/f+f=44 equation:

8+2/f+f=44

We move all terms to the left:

8+2/f+f-(44)=0


Domain of the equation: f!=0

f∈R


We add all the numbers together, and all the variables

f+2/f-36=0

We multiply all the terms by the denominator


f*f-36*f+2=0

We add all the numbers together, and all the variables

-36f+f*f+2=0

Wy multiply elements

f^2-36f+2=0

a = 1; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·1·2
Δ = 1288
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:

$\sqrt{\Delta}=\sqrt{1288}=\sqrt{4*322}=\sqrt{4}*\sqrt{322}=2\sqrt{322}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{322}}{2*1}=\frac{36-2\sqrt{322}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{322}}{2*1}=\frac{36+2\sqrt{322}}{2}
$