F(x)=2x+5/x+7

Solution for F(x)=2x+5/x+7 equation:

(F)=2F+5/F+7

We move all terms to the left:

(F)-(2F+5/F+7)=0


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

F∈R


We get rid of parentheses

F-2F-5/F-7=0

We multiply all the terms by the denominator


F*F-2F*F-7*F-5=0

We add all the numbers together, and all the variables

-7F+F*F-2F*F-5=0

Wy multiply elements

F^2-2F^2-7F-5=0

We add all the numbers together, and all the variables

-1F^2-7F-5=0

a = -1; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·(-1)·(-5)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{29}}{2*-1}=\frac{7-\sqrt{29}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*-1}=\frac{7+\sqrt{29}}{-2}
$