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

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

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

We move all terms to the left:

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


Domain of the equation: 3F+4)!=0

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3F^2-6F^2-12F+1=0

We add all the numbers together, and all the variables

-3F^2-12F+1=0

a = -3; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-3)·1
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*-3}=\frac{12-2\sqrt{39}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*-3}=\frac{12+2\sqrt{39}}{-6}
$