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

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

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

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -4; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-4)·2
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*-4}=\frac{6-2\sqrt{17}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*-4}=\frac{6+2\sqrt{17}}{-8}
$