F(x)=4/2x+4

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

(F)=4/2F+4

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-4/2F-4=0

We multiply all the terms by the denominator


F*2F-4*2F-4=0

Wy multiply elements

2F^2-8F-4=0

a = 2; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·2·(-4)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*2}=\frac{8-4\sqrt{6}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*2}=\frac{8+4\sqrt{6}}{4}
$