F(x)=4x^2/2x+3

Solution for F(x)=4x^2/2x+3 equation:

(F)=4F^2/2F+3

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

-4F^2/2F+F-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4F^2+2F^2-6F=0

We add all the numbers together, and all the variables

-2F^2-6F=0

a = -2; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-2)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-2}=\frac{0}{-4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-2}=\frac{12}{-4}
=-3
$