F(x)=4x+4/3x+11

Solution for F(x)=4x+4/3x+11 equation:

(F)=4F+4/3F+11

We move all terms to the left:

(F)-(4F+4/3F+11)=0


Domain of the equation: 3F+11)!=0

F∈R


We get rid of parentheses

F-4F-4/3F-11=0

We multiply all the terms by the denominator


F*3F-4F*3F-11*3F-4=0

Wy multiply elements

3F^2-12F^2-33F-4=0

We add all the numbers together, and all the variables

-9F^2-33F-4=0

a = -9; b = -33; c = -4;
Δ = b2-4ac
Δ = -332-4·(-9)·(-4)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{105}}{2*-9}=\frac{33-3\sqrt{105}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{105}}{2*-9}=\frac{33+3\sqrt{105}}{-18}
$