F(n)=2n+7/4n-9

Solution for F(n)=2n+7/4n-9 equation:

(F)=2F+7/4F-9

We move all terms to the left:

(F)-(2F+7/4F-9)=0


Domain of the equation: 4F-9)!=0

F∈R


We get rid of parentheses

F-2F-7/4F+9=0

We multiply all the terms by the denominator


F*4F-2F*4F+9*4F-7=0

Wy multiply elements

4F^2-8F^2+36F-7=0

We add all the numbers together, and all the variables

-4F^2+36F-7=0

a = -4; b = 36; c = -7;
Δ = b2-4ac
Δ = 362-4·(-4)·(-7)
Δ = 1184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{74}}{2*-4}=\frac{-36-4\sqrt{74}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{74}}{2*-4}=\frac{-36+4\sqrt{74}}{-8}
$