F(p)=2p+3/p-5

Solution for F(p)=2p+3/p-5 equation:

(F)=2F+3/F-5

We move all terms to the left:

(F)-(2F+3/F-5)=0


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

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-1F^2+5F-3=0

a = -1; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·(-1)·(-3)
Δ = 13
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{13}}{2*-1}=\frac{-5-\sqrt{13}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*-1}=\frac{-5+\sqrt{13}}{-2}
$