F(x)=3x/5x+6

Solution for F(x)=3x/5x+6 equation:

(F)=3F/5F+6

We move all terms to the left:

(F)-(3F/5F+6)=0


Domain of the equation: 5F+6)!=0

F∈R


We get rid of parentheses

F-3F/5F-6=0

We multiply all the terms by the denominator


F*5F-3F-6*5F=0

We add all the numbers together, and all the variables

-3F+F*5F-6*5F=0

Wy multiply elements

5F^2-3F-30F=0

We add all the numbers together, and all the variables

5F^2-33F=0

a = 5; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·5·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*5}=\frac{0}{10}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*5}=\frac{66}{10}
=6+3/5
$