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

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

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

We move all terms to the left:

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


Domain of the equation: F+2-2F-3)!=0

We move all terms containing F to the left, all other terms to the right

F-2F-3)!=-2

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

3F^2+F-3=0

a = 3; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·3·(-3)
Δ = 37
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{-(1)-\sqrt{37}}{2*3}=\frac{-1-\sqrt{37}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*3}=\frac{-1+\sqrt{37}}{6}
$