F(6)=1/2x-2x+4

Solution for F(6)=1/2x-2x+4 equation:

(6)=1/2F-2F+4

We move all terms to the left:

(6)-(1/2F-2F+4)=0


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

F∈R


We add all the numbers together, and all the variables

-(-2F+1/2F+4)+6=0

We get rid of parentheses

2F-1/2F-4+6=0

We multiply all the terms by the denominator


2F*2F-4*2F+6*2F-1=0

Wy multiply elements

4F^2-8F+12F-1=0

We add all the numbers together, and all the variables

4F^2+4F-1=0

a = 4; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·4·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*4}=\frac{-4-4\sqrt{2}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*4}=\frac{-4+4\sqrt{2}}{8}
$