F(a)=3a-5/a+5

Solution for F(a)=3a-5/a+5 equation:

(F)=3F-5/F+5

We move all terms to the left:

(F)-(3F-5/F+5)=0


Domain of the equation: F+5)!=0

F∈R


We get rid of parentheses

F-3F+5/F-5=0

We multiply all the terms by the denominator


F*F-3F*F-5*F+5=0

We add all the numbers together, and all the variables

-5F+F*F-3F*F+5=0

Wy multiply elements

F^2-3F^2-5F+5=0

We add all the numbers together, and all the variables

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

a = -2; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-2)·5
Δ = 65
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{-(-5)-\sqrt{65}}{2*-2}=\frac{5-\sqrt{65}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-2}=\frac{5+\sqrt{65}}{-4}
$