F(10)=x+5/x-7

Solution for F(10)=x+5/x-7 equation:

(10)=F+5/F-7

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

-F-5/F+7+10=0

We multiply all the terms by the denominator


-F*F+7*F+10*F-5=0

We add all the numbers together, and all the variables

17F-F*F-5=0

Wy multiply elements

-1F^2+17F-5=0

a = -1; b = 17; c = -5;
Δ = b2-4ac
Δ = 172-4·(-1)·(-5)
Δ = 269
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{-(17)-\sqrt{269}}{2*-1}=\frac{-17-\sqrt{269}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{269}}{2*-1}=\frac{-17+\sqrt{269}}{-2}
$