F(x)=x1/2x+4

Solution for F(x)=x1/2x+4 equation:

(F)=F1/2F+4

We move all terms to the left:

(F)-(F1/2F+4)=0


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

F∈R


We get rid of parentheses

F-F1/2F-4=0

We multiply all the terms by the denominator


F*2F-F1-4*2F=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

2F^2-9F=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$