F(2)=x+1/4x-2

Solution for F(2)=x+1/4x-2 equation:

(2)=F+1/4F-2

We move all terms to the left:

(2)-(F+1/4F-2)=0


Domain of the equation: 4F-2)!=0

F∈R


We get rid of parentheses

-F-1/4F+2+2=0

We multiply all the terms by the denominator


-F*4F+2*4F+2*4F-1=0

Wy multiply elements

-4F^2+8F+8F-1=0

We add all the numbers together, and all the variables

-4F^2+16F-1=0

a = -4; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-4)·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{15}}{2*-4}=\frac{-16-4\sqrt{15}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{15}}{2*-4}=\frac{-16+4\sqrt{15}}{-8}
$