F(x)=3x+1/4x+2

Solution for F(x)=3x+1/4x+2 equation:

(F)=3F+1/4F+2

We move all terms to the left:

(F)-(3F+1/4F+2)=0


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

F∈R


We get rid of parentheses

F-3F-1/4F-2=0

We multiply all the terms by the denominator


F*4F-3F*4F-2*4F-1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -8; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-8)·(-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{-(-8)-4\sqrt{2}}{2*-8}=\frac{8-4\sqrt{2}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2}}{2*-8}=\frac{8+4\sqrt{2}}{-16}
$