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

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

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

We move all terms to the left:

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


Domain of the equation: 3F-1)!=0

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

F+2F/3F-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

3F^2-10F=0

a = 3; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·3·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*3}=\frac{20}{6}
=3+1/3
$