f(x)=2x+1/x-7

Solution for f(x)=2x+1/x-7 equation:

(F)=2F+1/F-7

We move all terms to the left:

(F)-(2F+1/F-7)=0


Domain of the equation: F-7)!=0

F∈R


We get rid of parentheses

F-2F-1/F+7=0

We multiply all the terms by the denominator


F*F-2F*F+7*F-1=0

We add all the numbers together, and all the variables

7F+F*F-2F*F-1=0

Wy multiply elements

F^2-2F^2+7F-1=0

We add all the numbers together, and all the variables

-1F^2+7F-1=0

a = -1; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-1)·(-1)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{5}}{2*-1}=\frac{-7-3\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{5}}{2*-1}=\frac{-7+3\sqrt{5}}{-2}
$