F(d)=4(d)-12/d+5

Solution for F(d)=4(d)-12/d+5 equation:

(F)=4(F)-12/F+5

We move all terms to the left:

(F)-(4(F)-12/F+5)=0


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

F∈R


We get rid of parentheses

F-4F+12/F-5=0

We multiply all the terms by the denominator


F*F-4F*F-5*F+12=0

We add all the numbers together, and all the variables

-5F+F*F-4F*F+12=0

Wy multiply elements

F^2-4F^2-5F+12=0

We add all the numbers together, and all the variables

-3F^2-5F+12=0

a = -3; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-3)·12
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-3}=\frac{18}{-6}
=-3
$