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)=0


Domain of the equation: 3F)!=0

F!=0/1

F!=0

F∈R


We get rid of parentheses

F+2F-1/3F=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

9F^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$