F(x)=4x+4/2x+5

Solution for F(x)=4x+4/2x+5 equation:

(F)=4F+4/2F+5

We move all terms to the left:

(F)-(4F+4/2F+5)=0


Domain of the equation: 2F+5)!=0

F∈R


We get rid of parentheses

F-4F-4/2F-5=0

We multiply all the terms by the denominator


F*2F-4F*2F-5*2F-4=0

Wy multiply elements

2F^2-8F^2-10F-4=0

We add all the numbers together, and all the variables

-6F^2-10F-4=0

a = -6; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·(-6)·(-4)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*-6}=\frac{8}{-12}
=-2/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*-6}=\frac{12}{-12}
=-1
$