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

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

(F)=2F/3F+5

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-2F/3F-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

3F^2-17F=0

a = 3; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·3·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*3}=\frac{34}{6}
=5+2/3
$