F(0)=3x/2x^2+3

Solution for F(0)=3x/2x^2+3 equation:

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

We move all terms to the left:

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


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

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3F/2F^2-3=0

We multiply all the terms by the denominator


-3F-3*2F^2=0

Wy multiply elements

-6F^2-3F=0

a = -6; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-6)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-6}=\frac{0}{-12}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-6}=\frac{6}{-12}
=-1/2
$