F(x)=2x-1/3x+5

Solution for F(x)=2x-1/3x+5 equation:

(F)=2F-1/3F+5

We move all terms to the left:

(F)-(2F-1/3F+5)=0


Domain of the equation: 3F+5)!=0

F∈R


We get rid of parentheses

F-2F+1/3F-5=0

We multiply all the terms by the denominator


F*3F-2F*3F-5*3F+1=0

Wy multiply elements

3F^2-6F^2-15F+1=0

We add all the numbers together, and all the variables

-3F^2-15F+1=0

a = -3; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-3)·1
Δ = 237
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{237}}{2*-3}=\frac{15-\sqrt{237}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{237}}{2*-3}=\frac{15+\sqrt{237}}{-6}
$